Skip to main content
Erschienen in: Optical and Quantum Electronics 7/2017

01.07.2017

New exact solutions of some nonlinear evolution equations of pseudoparabolic type

verfasst von: K. Hosseini, E. Yazdani Bejarbaneh, A. Bekir, M. Kaplan

Erschienen in: Optical and Quantum Electronics | Ausgabe 7/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper aims to conduct an analytical study into some nonlinear models of pseudoparabolic type, including the Oskolkov, Oskolkov–Benjamin–Bona–Mahony–Burgers, and Benjamin–Bona–Mahony–Peregrine–Burgers equations. A number of new exact solutions for these pseudoparabolic type equations have been derived based on the modified Kudryashov method that its calculations are performed in a symbolic computation system known as Maple.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Akcagil, S., Aydemir, T., Gozukizil, O.F.: Exact travelling wave solutions of nonlinear pseudoparabolic equations by using the G′/G expansion method. New Trends Math. Sci. 4, 51–66 (2016)MathSciNetCrossRef Akcagil, S., Aydemir, T., Gozukizil, O.F.: Exact travelling wave solutions of nonlinear pseudoparabolic equations by using the G′/G expansion method. New Trends Math. Sci. 4, 51–66 (2016)MathSciNetCrossRef
Zurück zum Zitat Ayati, Z., Hosseini, K., Mirzazadeh, M.: Application of Kudryashov and functional variable methods to the strain wave equation in microstructured solids. Nonlinear Eng. (2016). doi:10.1515/nleng-2016-0020 Ayati, Z., Hosseini, K., Mirzazadeh, M.: Application of Kudryashov and functional variable methods to the strain wave equation in microstructured solids. Nonlinear Eng. (2016). doi:10.​1515/​nleng-2016-0020
Zurück zum Zitat Bekir, A., Güner, Ö., Bhrawy, A.H., Biswas, A.: Solving nonlinear fractional differential equations using exp-function and G′/G expansion methods. Rom. J. Phys. 60, 360–378 (2015) Bekir, A., Güner, Ö., Bhrawy, A.H., Biswas, A.: Solving nonlinear fractional differential equations using exp-function and G′/G expansion methods. Rom. J. Phys. 60, 360–378 (2015)
Zurück zum Zitat Biswas, A., Mirzazadeh, M.: Dark optical solitons with power law nonlinearity using (G′/G)-expansion. Optik 125, 4603–4608 (2014)ADSCrossRef Biswas, A., Mirzazadeh, M.: Dark optical solitons with power law nonlinearity using (G′/G)-expansion. Optik 125, 4603–4608 (2014)ADSCrossRef
Zurück zum Zitat Bulut, H., Baskonus, H.M., Pandir, Y.: The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation. Abstr. Appl. Anal. 2013, 636802 (2013a)MathSciNet Bulut, H., Baskonus, H.M., Pandir, Y.: The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation. Abstr. Appl. Anal. 2013, 636802 (2013a)MathSciNet
Zurück zum Zitat Bulut, H., Pandir, Y., Baskonus, H.M.: Symmetrical hyperbolic Fibonacci function solutions of generalized Fisher equation with fractional order. AIP Conf. Proc. 1558, 1914 (2013b)ADSCrossRef Bulut, H., Pandir, Y., Baskonus, H.M.: Symmetrical hyperbolic Fibonacci function solutions of generalized Fisher equation with fractional order. AIP Conf. Proc. 1558, 1914 (2013b)ADSCrossRef
Zurück zum Zitat Bulut, H., Sulaiman, T.A., Baskonus, H.M.: New solitary and optical wave structures to the Korteweg–de Vries equation with dual-power law nonlinearity. Opt. Quant. Electron. 48, 564 (2016). doi:10.1007/s11082-016-0831-4 CrossRef Bulut, H., Sulaiman, T.A., Baskonus, H.M.: New solitary and optical wave structures to the Korteweg–de Vries equation with dual-power law nonlinearity. Opt. Quant. Electron. 48, 564 (2016). doi:10.​1007/​s11082-016-0831-4 CrossRef
Zurück zum Zitat Demiray, S.T., Pandir, Y., Bulut, H.: Generalized Kudryashov method for time-fractional differential equations. Abstr. Appl. Anal. 2014, 901540 (2014)MathSciNet Demiray, S.T., Pandir, Y., Bulut, H.: Generalized Kudryashov method for time-fractional differential equations. Abstr. Appl. Anal. 2014, 901540 (2014)MathSciNet
Zurück zum Zitat Ekici, M., Mirzazadeh, M., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Solitons in optical metamaterials with fractional temporal evolution. Optik 127, 10879–10897 (2016)ADSCrossRef Ekici, M., Mirzazadeh, M., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Solitons in optical metamaterials with fractional temporal evolution. Optik 127, 10879–10897 (2016)ADSCrossRef
Zurück zum Zitat Guner, O., Bekir, A., Bilgil, H.: A note on exp-function method combined with complex transform method applied to fractional differential equations. Adv. Nonlinear Anal. 4, 201–208 (2015)MathSciNetMATH Guner, O., Bekir, A., Bilgil, H.: A note on exp-function method combined with complex transform method applied to fractional differential equations. Adv. Nonlinear Anal. 4, 201–208 (2015)MathSciNetMATH
Zurück zum Zitat Guner, O., Aksoy, E., Bekir, A., Cevikel, A.C.: Different methods for (3 + 1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov equation. Comput. Math Appl. 71, 1259–1269 (2016)MathSciNetCrossRef Guner, O., Aksoy, E., Bekir, A., Cevikel, A.C.: Different methods for (3 + 1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov equation. Comput. Math Appl. 71, 1259–1269 (2016)MathSciNetCrossRef
Zurück zum Zitat Hosseini, K., Ayati, Z.: Exact solutions of space-time fractional EW and modified EW equations using Kudryashov method. Nonlinear Sci. Lett. A 7, 58–66 (2016) Hosseini, K., Ayati, Z.: Exact solutions of space-time fractional EW and modified EW equations using Kudryashov method. Nonlinear Sci. Lett. A 7, 58–66 (2016)
Zurück zum Zitat Hosseini, K., Gholamin, P.: Feng’s first integral method for analytic treatment of two higher dimensional nonlinear partial differential equations. Differ. Equ. Dyn. Syst. 23, 317–325 (2015)MathSciNetCrossRefMATH Hosseini, K., Gholamin, P.: Feng’s first integral method for analytic treatment of two higher dimensional nonlinear partial differential equations. Differ. Equ. Dyn. Syst. 23, 317–325 (2015)MathSciNetCrossRefMATH
Zurück zum Zitat Hosseini, K., Ansari, R., Gholamin, P.: Exact solutions of some nonlinear systems of partial differential equations by using the first integral method. J. Math. Anal. Appl. 387, 807–814 (2012)MathSciNetCrossRefMATH Hosseini, K., Ansari, R., Gholamin, P.: Exact solutions of some nonlinear systems of partial differential equations by using the first integral method. J. Math. Anal. Appl. 387, 807–814 (2012)MathSciNetCrossRefMATH
Zurück zum Zitat Hosseini, K., Sadeghi, F., Ansari, R.: First integral method for solving nonlinear physical systems of partial differential equations. J. Nat. Sci. Sustain. Tech. 8, 391–400 (2014) Hosseini, K., Sadeghi, F., Ansari, R.: First integral method for solving nonlinear physical systems of partial differential equations. J. Nat. Sci. Sustain. Tech. 8, 391–400 (2014)
Zurück zum Zitat Hosseini, K., Mayeli, P., Ansari, R.: Modified Kudryashov method for solving the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities. Optik 130, 737–742 (2017a)ADSCrossRef Hosseini, K., Mayeli, P., Ansari, R.: Modified Kudryashov method for solving the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities. Optik 130, 737–742 (2017a)ADSCrossRef
Zurück zum Zitat Hosseini, K., Bekir, A., Ansari, R.: New exact solutions of the conformable time-fractional Cahn–Allen and Cahn–Hilliard equations using the modified Kudryashov method. Optik 132, 203–209 (2017b)ADSCrossRef Hosseini, K., Bekir, A., Ansari, R.: New exact solutions of the conformable time-fractional Cahn–Allen and Cahn–Hilliard equations using the modified Kudryashov method. Optik 132, 203–209 (2017b)ADSCrossRef
Zurück zum Zitat Jawad, A.J.M., Petkovic, M.D., Biswas, A.: Modified simple equation method for nonlinear evolution equations. Appl. Math. Comput. 217, 869–877 (2010)MathSciNetMATH Jawad, A.J.M., Petkovic, M.D., Biswas, A.: Modified simple equation method for nonlinear evolution equations. Appl. Math. Comput. 217, 869–877 (2010)MathSciNetMATH
Zurück zum Zitat Kaplan, M., Bekir, A., Akbulut, A., Aksoy, E.: The modified simple equation method for nonlinear fractional differential equations. Rom. J. Phys. 60, 1374–1383 (2015) Kaplan, M., Bekir, A., Akbulut, A., Aksoy, E.: The modified simple equation method for nonlinear fractional differential equations. Rom. J. Phys. 60, 1374–1383 (2015)
Zurück zum Zitat Khan, K., Ali Akbar, M., Rashidi, M.M., Zamanpour, I.: Exact traveling wave solutions of an autonomous system via the enhanced (G′/G)-expansion method. Waves Random Complex Media 25, 644–655 (2015)ADSMathSciNetCrossRef Khan, K., Ali Akbar, M., Rashidi, M.M., Zamanpour, I.: Exact traveling wave solutions of an autonomous system via the enhanced (G′/G)-expansion method. Waves Random Complex Media 25, 644–655 (2015)ADSMathSciNetCrossRef
Zurück zum Zitat Kudryashov, N.A.: One method for finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 2248–2253 (2012)ADSMathSciNetCrossRefMATH Kudryashov, N.A.: One method for finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 2248–2253 (2012)ADSMathSciNetCrossRefMATH
Zurück zum Zitat Mirzazadeh, M., Ekici, M., Zhou, Q., Sonmezoglu, A.: Analytical study of solitons to the generalized resonant dispersive nonlinear Schrödinger’s equation with power law nonlinearity. Superlattices Microstruct. (2016). doi:10.1016/j.spmi.2016.12.003 Mirzazadeh, M., Ekici, M., Zhou, Q., Sonmezoglu, A.: Analytical study of solitons to the generalized resonant dispersive nonlinear Schrödinger’s equation with power law nonlinearity. Superlattices Microstruct. (2016). doi:10.​1016/​j.​spmi.​2016.​12.​003
Zurück zum Zitat Odabasi, M., Misirli, E.: On the solutions of the nonlinear fractional differential equations via the modified trial equation method. Math. Methods Appl. Sci. (2015). doi:10.1002/mma.3533 MATH Odabasi, M., Misirli, E.: On the solutions of the nonlinear fractional differential equations via the modified trial equation method. Math. Methods Appl. Sci. (2015). doi:10.​1002/​mma.​3533 MATH
Zurück zum Zitat Pandir, Y., Gurefe, Y., Misirli, E.: The extended trial equation method for some time fractional differential equations. Discrete Dyn. Nat. Soc. 2013, 491359 (2013)MathSciNetCrossRefMATH Pandir, Y., Gurefe, Y., Misirli, E.: The extended trial equation method for some time fractional differential equations. Discrete Dyn. Nat. Soc. 2013, 491359 (2013)MathSciNetCrossRefMATH
Zurück zum Zitat Ryabov, P.N.: Exact solutions of the Kudryashov–Sinelshchikov equation. Appl. Math. Comput. 217, 3585–3590 (2010)MathSciNetMATH Ryabov, P.N.: Exact solutions of the Kudryashov–Sinelshchikov equation. Appl. Math. Comput. 217, 3585–3590 (2010)MathSciNetMATH
Zurück zum Zitat Saha, R.S.: New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods. Chin. Phys. B 25, 040204 (2016)ADSCrossRef Saha, R.S.: New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods. Chin. Phys. B 25, 040204 (2016)ADSCrossRef
Zurück zum Zitat Sahoo, S., Saha, S.: Ray, Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques (G′/G)-expansion method and improved (G′/G)-expansion method. Phys. A 448, 265–282 (2016)MathSciNetCrossRef Sahoo, S., Saha, S.: Ray, Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques (G′/G)-expansion method and improved (G′/G)-expansion method. Phys. A 448, 265–282 (2016)MathSciNetCrossRef
Zurück zum Zitat Taghizadeh, N., Zhou, Q., Ekici, M., Mirzazadeh, M.: Soliton solutions for Davydov solitons in α-helix proteins. Superlattices Microstruct. 102, 323–341 (2017)ADSCrossRef Taghizadeh, N., Zhou, Q., Ekici, M., Mirzazadeh, M.: Soliton solutions for Davydov solitons in α-helix proteins. Superlattices Microstruct. 102, 323–341 (2017)ADSCrossRef
Zurück zum Zitat Younis, M.: The first integral method for time-space fractional differential equations. J. Adv. Phys. 2, 220–223 (2013)CrossRef Younis, M.: The first integral method for time-space fractional differential equations. J. Adv. Phys. 2, 220–223 (2013)CrossRef
Zurück zum Zitat Younis, M.: A new approach for the exact solutions of nonlinear equations of fractional order via modified simple equation method. Appl. Math. 5, 1927–1932 (2014)CrossRef Younis, M.: A new approach for the exact solutions of nonlinear equations of fractional order via modified simple equation method. Appl. Math. 5, 1927–1932 (2014)CrossRef
Zurück zum Zitat Younis, M., Rizvi, S.T.R.: Dispersive dark optical soliton in (2 + 1)-dimensions by (G′/G)-expansion with dual-power law nonlinearity. Optik 126, 5812–5814 (2015)ADSCrossRef Younis, M., Rizvi, S.T.R.: Dispersive dark optical soliton in (2 + 1)-dimensions by (G′/G)-expansion with dual-power law nonlinearity. Optik 126, 5812–5814 (2015)ADSCrossRef
Zurück zum Zitat Younis, M., Zafar, A.: Exact solution to nonlinear differential equations of fractional order via (G/G′)-expansion method. Appl. Math. 5, 1–6 (2014)CrossRef Younis, M., Zafar, A.: Exact solution to nonlinear differential equations of fractional order via (G/G′)-expansion method. Appl. Math. 5, 1–6 (2014)CrossRef
Zurück zum Zitat Zayed, E.M.E., Alurrfi, K.A.E.: The modified Kudryashov method for solving some seventh order nonlinear PDEs in mathematical physics. World J. Model. Simul. 11, 308–319 (2015) Zayed, E.M.E., Alurrfi, K.A.E.: The modified Kudryashov method for solving some seventh order nonlinear PDEs in mathematical physics. World J. Model. Simul. 11, 308–319 (2015)
Metadaten
Titel
New exact solutions of some nonlinear evolution equations of pseudoparabolic type
verfasst von
K. Hosseini
E. Yazdani Bejarbaneh
A. Bekir
M. Kaplan
Publikationsdatum
01.07.2017
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 7/2017
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-017-1070-z

Weitere Artikel der Ausgabe 7/2017

Optical and Quantum Electronics 7/2017 Zur Ausgabe

Neuer Inhalt