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Optical and Quantum Electronics

Erschienen in:

01.02.2023

Study of mixed derivative nonlinear Schrödinger equation for rogue and lump waves, breathers and their interaction solutions with Kerr law

verfasst von: Syed T. R. Rizvi, Aly R. Seadawy, Syed K. Naqvi, Syed Oan Abbas

Erschienen in: Optical and Quantum Electronics | Ausgabe 2/2023

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Abstract

This paper studies various forms of analytical solutions for mixed derivative nonlinear Schrödinger equation (MD-NLSE) which is used extensively in optical fiber. Our aim is to obtain lump solution (which is analytic in all directions), lump with one kink, rogue waves, periodic waves and multi-wave solutions for our governing model. We also discuss the interaction between periodic and lump, breather wave (which is a localized periodic wave solution of either discrete lattice or continuous media mathematical models), generalized breather, Ma-breather, Kuznetsov-Ma-breather and their corresponding rogue waves. At the end, we also present the dynamical behaviour of our solutions in terms of graphs in various dimensions.

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Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and continuous nonlinear Schrödinger systems, vol. 302. Cambridge University Press (2004)MATH

Ahmad, S., Ashraf, R., Seadawy, A.R., Rizvi, S.T.R., Younis, M., Althobaiti, A., El-Shehawi, A.M.: Lump, multiwave, kinky breathers, interactional solutions and stability analysis for (2+1)-rth dispersionless Dym equation. Results in Physics 25, 104160 (2021)

Ahmed, Iftikhar, Seadawy, Aly R., Dianchen, Lu.: Kinky breathers, W-shaped and multi-peak solitons interaction in (2+1)-dimensional nonlinear Schrodinger’s equation with kerr law of nonlinearity. The European Physical Journal Plus 134(120), 1–11 (2019)

Akhmediev, N.N., Eleonskii, V.M., Kulagin, N.E.: Exact first-order solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 72, 809818 (1987)

Akram, U., Aly, R., Seadawy, S.T., Rizvi, R., Younis, M., Althobaiti, S., Sayed, S.: Traveling waves solutions for the fractional Wazwaz Benjamin Bona Mahony model in arising shallow water waves. Results Phys. 20, 103725 (2021)

Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Milovic, D., Moraru, L., Savescu, M., Biswas, A.: Optical solitons with polynomial and triple power law nonlinearities and spatio-temporal dispersion. Proc. Romanian Acad. 15, 235–240 (2014)MathSciNet

Bilal, M., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Zahed, H.: Dispersive of propagation wave solution to unidirectional shallow water wave Dullin Gottwald Holm system and modulation instability analysis. Math. Methods Appl. Sci. 44, 40944104 (2021)MathSciNetMATH

Binder, P., Abraimov, D., Ustinov, A.V.: Observation of breathers in josephson ladders. Phys. Rev. Lett. 84(4), 745 (2000)ADS

Chabchoub, A., Hoffmann, N., Onorato, M., Akhmediev, N.: Super rogue waves: observation of a higher-order breather in water waves. Phys. Rev. X 2, 011015 (2012)

Deng, Yj., Jia, Ry., Lin, J.: Lump and mixed rogue-soliton solutions of the (2+1)-dimensional Mel’nikov system. Complexity 2019, 1–9 (2019)MATH

Dianchen, Lu.: Bright-Dark optical soliton and dispersive elliptic function solutions of unstable nonlinear Schrodinger equation and its applications. Opt. Quant. Electron. 50(23), 1–10 (2018)

Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nat. Photonics 8, 755764 (2014)

Guan, W.Y., Li, B.Q.: New observation on the breather for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in inhomogeneous optical fiber. Optik 181, 853–861 (2019)ADS

Guan, X., Liu, W., Zhou, Q., Biswas, A.: Some lump solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation. Appl. Math. Comput. 366, 124757 (2020)MathSciNetMATH

Hao, H.Q., Zhang, J.W., Guo, R.: Soliton and breather solutions for the mixed nonlinear Schrödinger equation via \(N\)-Fold Darboux transformation. J. Appl. Math. 2014, 7 (2014)MATH

Khater, A.H., Helal, M.A., Seadawy, A.R.: General soliton solutions of n-dimensional nonlinear Schrödinger equation. IL Nuovo Cimento 115B, 1303–1312 (2000)ADS

Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N., Dudley, J.M.: The Peregrine soliton in nonlinear fibre optics. Nat. Phys. 6(10), 790–795 (2010)

Kol, G.R., Kingni, S.T., Woafo, P.: Rogue waves in Lugiato-Lefever equation with variable coefficients. Open Phys. 12(11), 767–772 (2014)ADS

Kuznetsov, E.A., Li, B.Q.: Solitons in parametrically unstable plasma. Sov. Phys. Dokl. 22, 507–508 (1977)ADS

Li, B.Q., Ma, Y.L.: Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation. Appl. Math. Comput. 386, 125469 (2020)MathSciNetMATH

Liu, J.G., Xiong, W.P.: Multi-wave, breather wave and lump solutions of the Boiti-Leon-Manna-Pempinelli equation with variable coefficients. Results in Physics 19, 103532 (2020)

Mylonas, I.K., Ward, C.B., Kevrekidis, P.G., Rothos, V.M., Frantzeskakis, D.J.: Asymptotic expansions and solitons of the Camassa-Holm-nonlinear Schrödinger equation. Phys. Lett. A 381(48), 3965–3971 (2017)ADSMathSciNetMATH

Peng, Y.Z.: Exact periodic wave solutions to the Melnikov equation. Zeitschrift Für Naturforschung A 60(5), 321–327 (2005)ADS

Rehman, S.U., Aly, R., Seadawy, M., Younis, S.T., Rizvi, R.: On study of modulation instability and optical soliton solutions: the chiral nonlinear Schrödinger dynamical equation. Opt. Quant. Electron. 53, 411 (2021)

Ren, B., Lin, J., Lou, Z.M.: A new nonlinear equation with lump-soliton, lump-periodic, and lump-periodic-soliton solutions. Complexity 2019, 1–10 (2019a)MATH

Ren, B., Lin, J., Lou, Z.-M.: A new nonlinear equation with lump-soliton, lump-periodic, and lump-periodic-soliton solutions. Complexity 2019, 4072754 (2019b)MATH

Rizvi, S.T.R., Seadawy, A.R., Ahmed, S., Younis, M., Ali, K.: Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation. Chaos Solitons Fractals 151, 111251 (2021a)MATH

Rizvi, S.T.R., Seadawy, A. R., Younis, M., Ali, K., Iqbal, H.: Lump-soliton, lump-multi soliton and lump-periodic solutions of a generalized hyperelastic rod equation. Mod. Phys. Lett. B 35(11), 2150188 (2021b)ADS

Seadawy, A. R., Cheemaa, N.: Some new families of spiky solitary waves of one-dimensional higher-order K-dV equation with power law nonlinearity in plasma physics, Indian Journal. Physics 94, 117–126 (2020)

Seadawy, A. R., Iqbal, M., Lu, D.: Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsive-Petviashvili modified equal width dynamical equation. Comput. Math. Appl. 78, 3620–3632 (2019)MathSciNetMATH

Seadawy, A. R., Arshad, M., Lu, D.: The weakly nonlinear wave propagation theory for the Kelvin-Helmholtz instability in magnetohydrodynamics flows. Chaos Solitons Fractals 139, 110141 (2020)MathSciNetMATH

Seadawy, A. R., Rizvi, S.T.R., Ahmad, S., Younis, M., Baleanu, D.: Lump, lump-one stripe, multiwave and breather solutions for the Hunter-Saxton equation, Open. Physics 19(1), 1–10 (2021a)

Seadawy, A. R., Rehman, S.U., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modeled with Pochhammer-Chree equation and its modulation instability analysis. Phys. Scr. 96(4), 045202 (2021b)ADS

Sulem, C., Sulem, P.L.: The nonlinear Schrödinger equation: self-focusing and wave collapse, vol. 139. Springer Science and Business Media (2007)MATH

Tang, Y., Tao, S., Guan, Q.: Lump solitons and the interaction phenomena of them for two classes of nonlinear evolution equations. Comput. Math. Appl. 72(9), 2334–2342 (2016)MathSciNetMATH

Tao, Y., He, J.: Multisolitons, breathers, and rogue waves for the HIROTA equation generated by Darboux transformation. Phys. Rev. E 85(2), 026601 (2012)ADS

Wang, M., Zhou, Y., Li, Z.: Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys. Lett. A 216, 67–75 (1996)ADSMATH

Yang, J.Y., Ma, W.X., Qin, Z.: Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation. Anal. Math. Phys. 8(3), 427–436 (2018)MathSciNetMATH

Yildirim, Y., Celik, N., Yasar, E.: Nonlinear Schrödinger equations with spatio-temporal dispersion in Kerr, parabolic, power and dual power law media: A novel extended Kudryashov’s algorithm and soliton solutions. Results Phys. 7, 3116–3123 (2017)ADS

Yin, H.M., Chow, K.W.: Breathers, cascading instabilities and Fermi-Pasta-Ulam-Tsingou recurrence of the derivative nonlinear Schrödinger equation: Effects of ‘self-steepening’ nonlinearity. Phys. D 428, 133033 (2021)MATH

Yin, H.M., Pan, Q., Chow, K.W.: Four-wave mixing and coherently coupled Schrödinger equations: Cascading processes and Fermi-Pasta-Ulam-Tsingou recurrence. Chaos 31, 083117 (2021). https://doi.org/10.1063/5.0051584ADSCrossRef

Yin, H.M., Pan, Q., Chow, K.W.: The Fermi-Pasta-Ulam-Tsingou recurrence for discrete systems: Cascading mechanism and machine learning for the Ablowitz-Ladik equation. Commun. Nonlinear Sci. Numer. Simul. 114, 106664 (2022a)MathSciNetMATH

Yin, H.M., Pan, Q., Chow, K.W.: Doubly periodic solutions and breathers of the Hirota equation: recurrence, cascading mechanism and spectral analysis. Nonlinear Dyn. (2022b). https://doi.org/10.1007/s11071-022-07799-4CrossRef

Yua, F., Yan, Z.: New rogue waves and dark-bright soliton solutions for a coupled nonlinear Schrödinger equation with variable coefficients. Appl. Math. Comput. 233, 351–358 (2014)MathSciNetMATH

Zakharov, V.E., Gelash, A.A.: Nonlinear stage of modulation instability. Phys. Rev. Lett. 111, 054101 (2013)ADS

Zhang, W.: Generalized variational principle for long water-wave equation by He’s Semi-Inverse method. Math. Probl. Eng. 2009, 1–5 (2009)ADSMathSciNet

Zhang, Y., Sun, Y., Xiang, W.: The rogue waves of the KP equation with self-consistent sources. Appl. Math. Comput. 263, 204–213 (2015)MathSciNetMATH

Zhou, Y., Manukure, S., Ma, W.X.: Lump and lump-soliton solutions to the Hirota-Satsuma-Ito equation. Commun. Nonlinear Sci. Numer. Simulat. 68, 56–62 (2019)ADSMathSciNetMATH

Titel: Study of mixed derivative nonlinear Schrödinger equation for rogue and lump waves, breathers and their interaction solutions with Kerr law
verfasst von: Syed T. R. Rizvi
Aly R. Seadawy
Syed K. Naqvi
Syed Oan Abbas
Publikationsdatum: 01.02.2023
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 2/2023
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-022-04415-y

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