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Erschienen in: Optical and Quantum Electronics 3/2018

01.03.2018

On the bright and singular optical solitons to the (\(2+1\))-dimensional NLS and the Hirota equations

verfasst von: Hasan Bulut, Tukur Abdulkadir Sulaiman, Haci Mehmet Baskonus, Tolga Aktürk

Erschienen in: Optical and Quantum Electronics | Ausgabe 3/2018

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Abstract

This study constructs bright and singular optical solitons the (\(2+1\))-dimensional NLSE and the Hirota equation by utilizing the new sine-Gordon expansion method. The parametric conditions for the existence of valid solitons are given. We give the variations of solitary and periodic wave solutions that depend on the parameters. We present the 2D, 3D and contour graphs to represent the kind of solutions secured in this study.

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Literatur
Zurück zum Zitat Agrawal, G.P.: Nonlinear Fiber Optics, (Optics and Photonics), 2nd edn. Academic Press, San Diego (1995) Agrawal, G.P.: Nonlinear Fiber Optics, (Optics and Photonics), 2nd edn. Academic Press, San Diego (1995)
Zurück zum Zitat Ali, A., Seadawy, A.R., Lu, D.: Soliton solutions of the nonlinear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear Schrödinger equation and their modulation instability analysis. Optik-Int. J. Light Electron Opt. 145, 79–88 (2017)CrossRef Ali, A., Seadawy, A.R., Lu, D.: Soliton solutions of the nonlinear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear Schrödinger equation and their modulation instability analysis. Optik-Int. J. Light Electron Opt. 145, 79–88 (2017)CrossRef
Zurück zum Zitat Arbabi, S., Najafi, M.: Exact solitary wave solutions of the complex nonlinear Schrödinger equations. Optik-Int. J. Light Electron Opt. 127(11), 4682–4688 (2016)CrossRef Arbabi, S., Najafi, M.: Exact solitary wave solutions of the complex nonlinear Schrödinger equations. Optik-Int. J. Light Electron Opt. 127(11), 4682–4688 (2016)CrossRef
Zurück zum Zitat Arnous, A.H., Mahmood, S.A., Younis, M.: Dynamics of optical solitons in dual-core fibers via two integration schemes. Superlattices Microstruct. 106, 156–162 (2017)ADSCrossRef Arnous, A.H., Mahmood, S.A., Younis, M.: Dynamics of optical solitons in dual-core fibers via two integration schemes. Superlattices Microstruct. 106, 156–162 (2017)ADSCrossRef
Zurück zum Zitat Baskonus, H.M., Sulaiman, T.A., Bulut, H.: On the novel wave behaviors to the nonlinear Maccari’s system with complex structure. Optik-Int. J. Light Electron Opt. 131, 1036–1043 (2017a)CrossRef Baskonus, H.M., Sulaiman, T.A., Bulut, H.: On the novel wave behaviors to the nonlinear Maccari’s system with complex structure. Optik-Int. J. Light Electron Opt. 131, 1036–1043 (2017a)CrossRef
Zurück zum Zitat Baskonus, H.M., Bulut, H., Sulaiman, T.A.: New solitary wave solutions to the (\(2+1\))-dimensional Calogero–Bogoyavlenskii-Schiff and the Kadomtsev–Petviashvili hierarchy equations. Indian J. Phys. 135, 327–336 (2017b) Baskonus, H.M., Bulut, H., Sulaiman, T.A.: New solitary wave solutions to the (\(2+1\))-dimensional Calogero–Bogoyavlenskii-Schiff and the Kadomtsev–Petviashvili hierarchy equations. Indian J. Phys. 135, 327–336 (2017b)
Zurück zum Zitat Baskonus, H.M., Sulaiman, T.A., Bulut, H., Akturk, T.: Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schrödinger equation with \(\delta\)-potential. Superlattices Microstruct. 115, 19–29 (2018)ADSCrossRef Baskonus, H.M., Sulaiman, T.A., Bulut, H., Akturk, T.: Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schrödinger equation with \(\delta\)-potential. Superlattices Microstruct. 115, 19–29 (2018)ADSCrossRef
Zurück zum Zitat Biswas, A., Mirzazadeh, M., Eslami, M., Milovic, D., Belic, M.: Solitons in optical metamaterials by functional variable method and first integral approach. Frequenz 68(11–12), 525–530 (2014)ADS Biswas, A., Mirzazadeh, M., Eslami, M., Milovic, D., Belic, M.: Solitons in optical metamaterials by functional variable method and first integral approach. Frequenz 68(11–12), 525–530 (2014)ADS
Zurück zum Zitat Bulut, H., Sulaiman, T.A., Baskonus, H.M.: On the new soliton and optical wave structures to some nonlinear evolution equations. Eur. Phys. J. Plus 132, 459 (2017a)CrossRef Bulut, H., Sulaiman, T.A., Baskonus, H.M.: On the new soliton and optical wave structures to some nonlinear evolution equations. Eur. Phys. J. Plus 132, 459 (2017a)CrossRef
Zurück zum Zitat Bulut, H., Sulaiman, T.A., Baskonus, H.M., Erdogan, F.: On the new hyperbolic and trigonometric structures to the simplified MCH and SRLW equations. Eur. Phys. J. Plus 132, 350 (2017b)CrossRef Bulut, H., Sulaiman, T.A., Baskonus, H.M., Erdogan, F.: On the new hyperbolic and trigonometric structures to the simplified MCH and SRLW equations. Eur. Phys. J. Plus 132, 350 (2017b)CrossRef
Zurück zum Zitat Bulut, H., Sulaiman, T.A., Demirdag, B.: Dynamics of soliton solutions in the chiral nonlinear Schrödinger equations. Nonlinear Dyn. 91(3), 1985–1991 (2018)CrossRef Bulut, H., Sulaiman, T.A., Demirdag, B.: Dynamics of soliton solutions in the chiral nonlinear Schrödinger equations. Nonlinear Dyn. 91(3), 1985–1991 (2018)CrossRef
Zurück zum Zitat Chen, Y., Yan, Z.: New exact solutions of (\(2+1\))-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos, Solitons Fractals 26, 399–406 (2005)ADSMathSciNetCrossRefMATH Chen, Y., Yan, Z.: New exact solutions of (\(2+1\))-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos, Solitons Fractals 26, 399–406 (2005)ADSMathSciNetCrossRefMATH
Zurück zum Zitat Ekici, M., Mirzazadeh, M., Eslami, M.: Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion. Nonlinear Dyn. 84(2), 669–676 (2016)MathSciNetCrossRefMATH Ekici, M., Mirzazadeh, M., Eslami, M.: Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion. Nonlinear Dyn. 84(2), 669–676 (2016)MathSciNetCrossRefMATH
Zurück zum Zitat Eslami, M.: Solitary wave solutions for perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity under the DAM. Optik-Int. J. Light Electron Opt. 126(13), 1312–1317 (2015)CrossRef Eslami, M.: Solitary wave solutions for perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity under the DAM. Optik-Int. J. Light Electron Opt. 126(13), 1312–1317 (2015)CrossRef
Zurück zum Zitat Eslami, M.: Soliton-like solutions for the coupled Schrodinger-Boussinesq equation. Optik-Int. J. Light Electron Opt. 126(23), 3987–3991 (2016a)CrossRef Eslami, M.: Soliton-like solutions for the coupled Schrodinger-Boussinesq equation. Optik-Int. J. Light Electron Opt. 126(23), 3987–3991 (2016a)CrossRef
Zurück zum Zitat Eslami, M.: Trial solution technique to chiral nonlinear Schrödinger equation in (1+2)-dimensions. Nonlinear Dyn. 85(2), 813–816 (2016b)CrossRef Eslami, M.: Trial solution technique to chiral nonlinear Schrödinger equation in (1+2)-dimensions. Nonlinear Dyn. 85(2), 813–816 (2016b)CrossRef
Zurück zum Zitat Eslami, M.: Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations. Appl. Math. Comput. 285, 141–148 (2016c)MathSciNet Eslami, M.: Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations. Appl. Math. Comput. 285, 141–148 (2016c)MathSciNet
Zurück zum Zitat Eslami, M., Mirzazadeh, M.: First integral method to look for exact solutions of a variety of Boussinesq-like equations. Ocean Eng. 83, 133–137 (2014)CrossRef Eslami, M., Mirzazadeh, M.: First integral method to look for exact solutions of a variety of Boussinesq-like equations. Ocean Eng. 83, 133–137 (2014)CrossRef
Zurück zum Zitat Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83(1–2), 731–738 (2016)MathSciNetCrossRefMATH Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83(1–2), 731–738 (2016)MathSciNetCrossRefMATH
Zurück zum Zitat Eslami, M., Neirameh, A.: New solitary and double periodic wave solutions for a generalized sinh-Gordon equation. Eur. Phys. J. Plus 129(4), 54 (2014)CrossRef Eslami, M., Neirameh, A.: New solitary and double periodic wave solutions for a generalized sinh-Gordon equation. Eur. Phys. J. Plus 129(4), 54 (2014)CrossRef
Zurück zum Zitat Eslami, M., Neirameh, A.: New exact solutions for higher order nonlinear Schrödinger equation in optical fibers. Opt. Quantum Electron. 50(1), 47 (2018)CrossRef Eslami, M., Neirameh, A.: New exact solutions for higher order nonlinear Schrödinger equation in optical fibers. Opt. Quantum Electron. 50(1), 47 (2018)CrossRef
Zurück zum Zitat Eslami, M., Rezazadeh, H.: The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo 53(3), 475–485 (2016)MathSciNetCrossRefMATH Eslami, M., Rezazadeh, H.: The first integral method for Wu-Zhang system with conformable time-fractional derivative. Calcolo 53(3), 475–485 (2016)MathSciNetCrossRefMATH
Zurück zum Zitat Eslami, M., Neyrame, A., Ebrahimi, M.: Explicit solutions of nonlinear (\(2+1\))-dimensional dispersive long wave equation. J. King Saud Univ. Sci. 24(1), 69–71 (2012)CrossRef Eslami, M., Neyrame, A., Ebrahimi, M.: Explicit solutions of nonlinear (\(2+1\))-dimensional dispersive long wave equation. J. King Saud Univ. Sci. 24(1), 69–71 (2012)CrossRef
Zurück zum Zitat Eslami, M., Mirzazadeh, M.A., Neirameh, A.: New exact wave solutions for Hirota equation. Pramana 84(1), 3–8 (2015)ADSCrossRef Eslami, M., Mirzazadeh, M.A., Neirameh, A.: New exact wave solutions for Hirota equation. Pramana 84(1), 3–8 (2015)ADSCrossRef
Zurück zum Zitat Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S.S.: Exact solutions to the space-time fractional Schrödinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation. Opt. Quantum Electron. 49(8), 279 (2017a)CrossRef Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S.S.: Exact solutions to the space-time fractional Schrödinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation. Opt. Quantum Electron. 49(8), 279 (2017a)CrossRef
Zurück zum Zitat Eslami, M., Khodadad, F.S., Nazari, F., Rezazadeh, H.: The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative. Opt. Quantum Electron. 49, 391 (2017b)CrossRef Eslami, M., Khodadad, F.S., Nazari, F., Rezazadeh, H.: The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative. Opt. Quantum Electron. 49, 391 (2017b)CrossRef
Zurück zum Zitat Gepreel, K.A.: Extended trial equation method for nonlinear coupled Schrodinger Boussinesq partial differential equations. J. Egypt. Math. Soc. 24, 381–391 (2016)MathSciNetCrossRefMATH Gepreel, K.A.: Extended trial equation method for nonlinear coupled Schrodinger Boussinesq partial differential equations. J. Egypt. Math. Soc. 24, 381–391 (2016)MathSciNetCrossRefMATH
Zurück zum Zitat Helal, M.A., Seadawy, A.R.: Exact soliton solutions of an D-dimensional nonlinear Schrödinger equation with damping and diffusive terms. Math. Phys. 62, 839–847 (2011)MathSciNetMATH Helal, M.A., Seadawy, A.R.: Exact soliton solutions of an D-dimensional nonlinear Schrödinger equation with damping and diffusive terms. Math. Phys. 62, 839–847 (2011)MathSciNetMATH
Zurück zum Zitat Khodadad, F.S., Nazari, F., Eslami, M., Rezazadeh, H.: Soliton solutions of the conformable fractional Zakharov–Kuznetsov equation with dual-power law nonlinearity. Opt. Quantum Electron. 49, 384 (2017)CrossRef Khodadad, F.S., Nazari, F., Eslami, M., Rezazadeh, H.: Soliton solutions of the conformable fractional Zakharov–Kuznetsov equation with dual-power law nonlinearity. Opt. Quantum Electron. 49, 384 (2017)CrossRef
Zurück zum Zitat Lü, X.: Madelung fluid description on a generalized mixed nonlinear Schrödinger equation. Nonlinear Dyn. 81, 239–247 (2015)CrossRefMATH Lü, X.: Madelung fluid description on a generalized mixed nonlinear Schrödinger equation. Nonlinear Dyn. 81, 239–247 (2015)CrossRefMATH
Zurück zum Zitat Mirzazadeh, M., Eslami, M., Biswas, A.: Soliton solutions of the generalized Klein–Gordon equation by using \((G^{^{\prime }}/G)\)-expansion method. Comput. Appl. Math. 33(3), 831–839 (2014)MathSciNetCrossRefMATH Mirzazadeh, M., Eslami, M., Biswas, A.: Soliton solutions of the generalized Klein–Gordon equation by using \((G^{^{\prime }}/G)\)-expansion method. Comput. Appl. Math. 33(3), 831–839 (2014)MathSciNetCrossRefMATH
Zurück zum Zitat Mirzazadeh, M., Eslami, M., Zerrad, E., Mahmood, M.F., Biswas, A., Belic, M.: Optical solitons in nonlinear directional couplers by sine-cosine function method and Bernoulli’s equation approach. Nonlinear Dyn. 81(4), 1933–1949 (2015a)MathSciNetCrossRefMATH Mirzazadeh, M., Eslami, M., Zerrad, E., Mahmood, M.F., Biswas, A., Belic, M.: Optical solitons in nonlinear directional couplers by sine-cosine function method and Bernoulli’s equation approach. Nonlinear Dyn. 81(4), 1933–1949 (2015a)MathSciNetCrossRefMATH
Zurück zum Zitat Najafi, M., Arbabi, S.: Traveling wave solutions for nonlinear Schrödinger equations. Optik-Int. J. Light Electron Opt. 126(23), 3992–3997 (2015)CrossRef Najafi, M., Arbabi, S.: Traveling wave solutions for nonlinear Schrödinger equations. Optik-Int. J. Light Electron Opt. 126(23), 3992–3997 (2015)CrossRef
Zurück zum Zitat Neirameh, A., Eslami, M.: An analytical method for finding exact solitary wave solutions of the coupled (\(2+1\))-dimensional Painlev\(\acute{e}\) Burgers equation. Sci. Iran. Trans. B. Mech. Eng. 25(2), 715 (2017) Neirameh, A., Eslami, M.: An analytical method for finding exact solitary wave solutions of the coupled (\(2+1\))-dimensional Painlev\(\acute{e}\) Burgers equation. Sci. Iran. Trans. B. Mech. Eng. 25(2), 715 (2017)
Zurück zum Zitat Pelinovsky, D.E.: Stability analysis of embedded solitons in the generalized third-order nonlinear Schrödinger equation. Chaos 15, 037115 (2015)ADSCrossRefMATH Pelinovsky, D.E.: Stability analysis of embedded solitons in the generalized third-order nonlinear Schrödinger equation. Chaos 15, 037115 (2015)ADSCrossRefMATH
Zurück zum Zitat Ray, S.S.: An application of the modified decomposition method for the solution of the coupled Klein-Gordon-Shrödinger equation. Commun. Nonlinear Sci. Numer. Simul. 13(7), 1311–1317 (2008)ADSMathSciNetCrossRefMATH Ray, S.S.: An application of the modified decomposition method for the solution of the coupled Klein-Gordon-Shrödinger equation. Commun. Nonlinear Sci. Numer. Simul. 13(7), 1311–1317 (2008)ADSMathSciNetCrossRefMATH
Zurück zum Zitat Ray, S.S.: On the soliton solution and Jacobi doubly periodic solution of the fractional coupled Schrödinger-KdV equation by a novel approach. Int. J. Nonlinear Sci. Numer. Simul. 16, 79–95 (2015)MathSciNetCrossRef Ray, S.S.: On the soliton solution and Jacobi doubly periodic solution of the fractional coupled Schrödinger-KdV equation by a novel approach. Int. J. Nonlinear Sci. Numer. Simul. 16, 79–95 (2015)MathSciNetCrossRef
Zurück zum Zitat Ray, S.S.: New double periodic exact solutions of the coupled Schrödinger-Boussinesq equations describing physical processes in laser and plasma physics. Chin. J. Phys. 55(5), 2039–2047 (2017)CrossRef Ray, S.S.: New double periodic exact solutions of the coupled Schrödinger-Boussinesq equations describing physical processes in laser and plasma physics. Chin. J. Phys. 55(5), 2039–2047 (2017)CrossRef
Zurück zum Zitat Scott, A.C.: Encyclopedia of Nonlinear Science. Taylor, Routledge, New York (2005)MATH Scott, A.C.: Encyclopedia of Nonlinear Science. Taylor, Routledge, New York (2005)MATH
Zurück zum Zitat Seadawy, A.R.: Stability analysis for two-dimensional ion-acoustic waves in quantum plasmas. Phys. Plasmas 21, 052107 (2014)ADSCrossRef Seadawy, A.R.: Stability analysis for two-dimensional ion-acoustic waves in quantum plasmas. Phys. Plasmas 21, 052107 (2014)ADSCrossRef
Zurück zum Zitat Seadawy, A.R.: Fractional solitary wave solutions of the nonlinear higher-order extended KdV equation in a stratified shear flow: Part I. Comput. Math. Appl. 70(4), 345–352 (2015a)MathSciNetCrossRef Seadawy, A.R.: Fractional solitary wave solutions of the nonlinear higher-order extended KdV equation in a stratified shear flow: Part I. Comput. Math. Appl. 70(4), 345–352 (2015a)MathSciNetCrossRef
Zurück zum Zitat Seadawy, A.R.: Approximation solutions of derivative nonlinear Schrödinger equation with computational applications by variational method. Eur. Phys. J. Plus 130, 182 (2015b)CrossRef Seadawy, A.R.: Approximation solutions of derivative nonlinear Schrödinger equation with computational applications by variational method. Eur. Phys. J. Plus 130, 182 (2015b)CrossRef
Zurück zum Zitat Seadawy, A.R.: Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma. Phys. A 439(1), 124–131 (2015c)MathSciNetCrossRef Seadawy, A.R.: Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma. Phys. A 439(1), 124–131 (2015c)MathSciNetCrossRef
Zurück zum Zitat Seadawy, A.R.: Stability analysis of traveling wave solutions for generalized coupled nonlinear KdV equations. Appl. Math. Inf. Sci. 10(1), 1–7 (2016a)MathSciNetCrossRef Seadawy, A.R.: Stability analysis of traveling wave solutions for generalized coupled nonlinear KdV equations. Appl. Math. Inf. Sci. 10(1), 1–7 (2016a)MathSciNetCrossRef
Zurück zum Zitat Seadawy, A.R.: Three-dimensional nonlinear modified Zakharov–Kuznetsov equation of ion-acoustic waves in a magnetized plasma. Comput. Math. Appl. 71(1), 201–212 (2016b)MathSciNetCrossRef Seadawy, A.R.: Three-dimensional nonlinear modified Zakharov–Kuznetsov equation of ion-acoustic waves in a magnetized plasma. Comput. Math. Appl. 71(1), 201–212 (2016b)MathSciNetCrossRef
Zurück zum Zitat Seadawy, A.R.: Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov–Kuznetsov equation in a magnetized electron-positron plasma. Phys. A 455, 44–51 (2016c)MathSciNetCrossRef Seadawy, A.R.: Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov–Kuznetsov equation in a magnetized electron-positron plasma. Phys. A 455, 44–51 (2016c)MathSciNetCrossRef
Zurück zum Zitat Seadawy, A.R.: Ion acoustic solitary wave solutions of two-dimensional nonlinear Kadomtsev–Petviashvili–Burgers equation in quantum plasma. Math. Method Appl. Sci. 40(5), 1598–1607 (2017a)ADSMathSciNetCrossRefMATH Seadawy, A.R.: Ion acoustic solitary wave solutions of two-dimensional nonlinear Kadomtsev–Petviashvili–Burgers equation in quantum plasma. Math. Method Appl. Sci. 40(5), 1598–1607 (2017a)ADSMathSciNetCrossRefMATH
Zurück zum Zitat Seadawy, A.R.: Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev–Petviashvili dynamical equation for dispersive shallow-water waves. Eur. Phys. J. Plus 132, 29 (2017b)CrossRef Seadawy, A.R.: Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev–Petviashvili dynamical equation for dispersive shallow-water waves. Eur. Phys. J. Plus 132, 29 (2017b)CrossRef
Zurück zum Zitat Seadawy, A.R.: The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrödinger equation and its solutions. Optik- Int. J. Light Electron Opt. 139, 31–43 (2017c)CrossRef Seadawy, A.R.: The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrödinger equation and its solutions. Optik- Int. J. Light Electron Opt. 139, 31–43 (2017c)CrossRef
Zurück zum Zitat Seadawy, A.R.: Modulation instability analysis for the generalized derivative higher order nonlinear Schrödinger equation and its the bright and dark soliton solutions. J. Electromagn. Waves Appl. 31(14), 1353–1362 (2017d)MathSciNetCrossRef Seadawy, A.R.: Modulation instability analysis for the generalized derivative higher order nonlinear Schrödinger equation and its the bright and dark soliton solutions. J. Electromagn. Waves Appl. 31(14), 1353–1362 (2017d)MathSciNetCrossRef
Zurück zum Zitat Seadawy, A.R.: Solitary wave solutions of two-dimensional nonlinear Kadomtsev–Petviashvili dynamic equation in dust-acoustic plasmas. Pramana J. Phys. 89, 49 (2017e)ADSCrossRef Seadawy, A.R.: Solitary wave solutions of two-dimensional nonlinear Kadomtsev–Petviashvili dynamic equation in dust-acoustic plasmas. Pramana J. Phys. 89, 49 (2017e)ADSCrossRef
Zurück zum Zitat Seadawy, A.R., Lu, D.: Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma. Results Phys. 6, 590–593 (2016)ADSCrossRef Seadawy, A.R., Lu, D.: Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma. Results Phys. 6, 590–593 (2016)ADSCrossRef
Zurück zum Zitat Seadawy, A.R., Lu, D.: Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability. Results Phys. 7, 43–48 (2017)CrossRef Seadawy, A.R., Lu, D.: Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability. Results Phys. 7, 43–48 (2017)CrossRef
Zurück zum Zitat Su, J.-J., Gao, Y.-T.: Dark solitons for a system of the (2+1)-dimensional coupled nonlinear Schrödinger equations with time-dependent coefficients in optical fibers. Superlattices Microstruct. 104, 498–508 (2017)ADSCrossRef Su, J.-J., Gao, Y.-T.: Dark solitons for a system of the (2+1)-dimensional coupled nonlinear Schrödinger equations with time-dependent coefficients in optical fibers. Superlattices Microstruct. 104, 498–508 (2017)ADSCrossRef
Zurück zum Zitat Wazwaz, A.M.: A study on linear and nonlinear Schrdinger equations by the variational iteration method. Chaos Solitons Frac. 37, 1136–1142 (2008)ADSCrossRefMATH Wazwaz, A.M.: A study on linear and nonlinear Schrdinger equations by the variational iteration method. Chaos Solitons Frac. 37, 1136–1142 (2008)ADSCrossRefMATH
Zurück zum Zitat Weisstein, E.W.: Concise Encyclopedia of Mathematics, 2nd edn. CRC Press, New York (2002)MATH Weisstein, E.W.: Concise Encyclopedia of Mathematics, 2nd edn. CRC Press, New York (2002)MATH
Zurück zum Zitat Xiang, R., Ling, L., Lü, X.: Some novel solutions for the two-coupled nonlinear Schrödinger equations. Appl. Math. Lett. 68, 163–170 (2017)MathSciNetCrossRefMATH Xiang, R., Ling, L., Lü, X.: Some novel solutions for the two-coupled nonlinear Schrödinger equations. Appl. Math. Lett. 68, 163–170 (2017)MathSciNetCrossRefMATH
Zurück zum Zitat Yang, X.J., Gao, F., Srivastava, H.M.: Exact travelling wave solutions for the local fractional two-dimensional burgers-type equations. Comput. Math. Appl. 73(2), 203–210 (2017)MathSciNetCrossRefMATH Yang, X.J., Gao, F., Srivastava, H.M.: Exact travelling wave solutions for the local fractional two-dimensional burgers-type equations. Comput. Math. Appl. 73(2), 203–210 (2017)MathSciNetCrossRefMATH
Zurück zum Zitat Younis, M., Cheemaa, N., Mahmood, S.A., Rizvi, S.T.R.: On optical solitons: the chiral nonlinear Schrödinger equation with perturbation and Bohm potential. Opt. Quant. Electron. 48, 542 (2016)CrossRef Younis, M., Cheemaa, N., Mahmood, S.A., Rizvi, S.T.R.: On optical solitons: the chiral nonlinear Schrödinger equation with perturbation and Bohm potential. Opt. Quant. Electron. 48, 542 (2016)CrossRef
Zurück zum Zitat Younis, M., Rehman, H., Rizv, S.T.R., Mahmood, S.A.: Dark and singular optical solitons perturbation with fractional temporal evolution. Superlattices Microstruct. 104, 525–531 (2017)ADSCrossRef Younis, M., Rehman, H., Rizv, S.T.R., Mahmood, S.A.: Dark and singular optical solitons perturbation with fractional temporal evolution. Superlattices Microstruct. 104, 525–531 (2017)ADSCrossRef
Zurück zum Zitat Zayed, E.M.E., Alurrfi, K.A.E.: Solitons and other solutions for two nonlinear Schrödinger equations using the new mapping method. Optik-Int. J. Light Electron Opt. 144, 132–148 (2017a)CrossRef Zayed, E.M.E., Alurrfi, K.A.E.: Solitons and other solutions for two nonlinear Schrödinger equations using the new mapping method. Optik-Int. J. Light Electron Opt. 144, 132–148 (2017a)CrossRef
Zurück zum Zitat Zayed, E.M.E., Al-Nowehy, A.G., Elshater, M.E.M.: Solitons and other solutions to nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity using several different techniques. Eur. Phys. J. Plus 132, 259 (2017b)CrossRef Zayed, E.M.E., Al-Nowehy, A.G., Elshater, M.E.M.: Solitons and other solutions to nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity using several different techniques. Eur. Phys. J. Plus 132, 259 (2017b)CrossRef
Zurück zum Zitat Zedan, H.A., Alaidarous, E., Shapll, S.: Erratum to: exact solutions for a perturbed nonlinear Shrödinger equation by using Bäcklund transformations. Nonlinear Dyn. 74(4), 1153–1153 (2013)CrossRef Zedan, H.A., Alaidarous, E., Shapll, S.: Erratum to: exact solutions for a perturbed nonlinear Shrödinger equation by using Bäcklund transformations. Nonlinear Dyn. 74(4), 1153–1153 (2013)CrossRef
Zurück zum Zitat Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Optical solitons with Biswas–Milovic equation by extended trial equation method. Nonlinear Dyn. 84(4), 1883–1900 (2016)MathSciNetCrossRefMATH Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Optical solitons with Biswas–Milovic equation by extended trial equation method. Nonlinear Dyn. 84(4), 1883–1900 (2016)MathSciNetCrossRefMATH
Metadaten
Titel
On the bright and singular optical solitons to the ()-dimensional NLS and the Hirota equations
verfasst von
Hasan Bulut
Tukur Abdulkadir Sulaiman
Haci Mehmet Baskonus
Tolga Aktürk
Publikationsdatum
01.03.2018
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 3/2018
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-018-1411-6

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