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Traveling Wave Solutions of Some Nonlinear Partial Equations

Year 2022, Volume: 10 Issue: 2, 301 - 312, 31.10.2022

Abstract

We apply the extended trial equation method (ETEM) to obtain exact solutions of (2+1) dimensional nonlinear electrical transmission line equation (NETLE) and Benjamin-Bona-Mahony-Peregrine (BBMP) equation in this study. We create some exact solutions like soliton solutions, rational, Jacobi elliptic, periodic wave solutions and hyperbolic function solutions of these equations via ETEM. Then, we present conclusions that we acquired thanks to this method.

References

  • [1] A.M. Wazwaz, The Hirota’s direct method and the tanh–coth method for multiplesoliton solutions of the Sawada–Kotera–Ito seventh-order equation, Applied Mathematics and Computation, 199 (2008), 133-138.
  • [2] F. Pelap, J. Kamga, A. Fomethe, A. Kenfack and M. Fave, Wave dynamics in a modified quintic complex Ginzburg-Landau system, Phys. Lett. A, 373 (2009), 1015-1018.
  • [3] Y. Pandir and A. Ekin, Dynamics of combined soliton solutions of unstable nonlinear Schrodinger equation with new version of the trial equation method, Chinese Journal of Physics, 67 (2020), 534-543.
  • [4] S.T.R. Rizvi, K. Ali, A. Sardar, M. Younis and A. Bekir, Symbolic computation and abundant travelling wave solutions to KdV-mKdV equation, Pramana, 88(1) (2017), 1-6.
  • [5] A. Irshad and S.T. Mohyud-Din, Tanh-Coth Method for Nonlinear Differantial Equations, Studies in Nonlinear Sciences, 3(1) (2012), 24-48.
  • [6] H.F. Ismael, A. Seadawy and H. Bulut, Construction of breather solutions and N-soliton for the higher order dimensional Caudrey– Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns, International Journal of Nonlinear Sciences and Numerical Simulation, (2021), 000010151520200169.
  • [7] H.F. Ismael and H. Bulut, Nonlinear dynamics of (2+1)-dimensional Bogoyavlenskii–Schieff equation arising in plasma physics, Mathematical Methods in the Aapplied Sciences, 44(13) (2021), 10321-10330.
  • [8] H.F. Ismael, A. Seadawy and H. Bulut, Rational solutions, and the interaction solutions to the (2+1)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation, International Journal of Computer Mathematics, 98(12) (2021), 2369-2377.
  • [9] H.F. Ismael, S.S. Atas, H. Bulut and M.S. Osman, Analytical solutions to the M-derivative resonant Davey–Stewartson equations, Modern Physics Letters B, 35(30) (2021), 2150455.
  • [10] Y. Pandir, Y. Gurefe, U. Kadak and E. Misirli, Classification of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstract and Applied Analysis, 2012 (2012), 1-16.
  • [11] H. Bulut, Y. Pandir and S. Tuluce Demiray, Exact Solutions of Nonlinear Schrodinger’s Equation with Dual Power-Law Nonlinearity by Extended Trial Equation Method, Waves in Random and Complex Media, 24(4) (2014), 439-451.
  • [12] S. Tuluce Demiray and H. Bulut, Some exact solutions of generalized Zakharov system, Waves in Random and Complex Media, 25(1) (2015), 75-90.
  • [13] S. Tuluce Demiray, Y. Pandir and H. Bulut, New Solitary Waves Solutions of Maccari System, Ocean Engineering, 103 (2015), 153-159.
  • [14] S. Tuluce Demiray, Y. Pandir and H. Bulut, New Soliton Solutions for Sasa-Satsuma Equation, Waves in Random and Complex Media, 25(3) (2015), 417-428.
  • [15] W. Kang-Jia and W. Guo-Dong, Periodic solution of the (2+1)-dimensional nonlinear electrical transmission line equation via variational method, Results in Physics, 20 (2021), 1-2.
  • [16] M.A. Kayum, S. Ara, H.K. Barman and M.A. Akbar, Soliton solutions to voltage analysis in nonlinear electrical transmission lines and electric signals in telegraph lines, Results in Physics, 18 (2020), 1-10.
  • [17] E. Tala-Tebue, D.C. Tsobgni-Fozap, A. Kenfack-Jiotsa and T.C. Kofane, Envelope periodic solutions for a discrete network with the Jacobi elliptic functions and the alternative (G0=G)-expansion method including the generalized Riccati equation, The European Physıcal Journal Plus, 129(136) (2014), 1-10.
  • [18] E. Tala-Tebue and E.M.E. Zayed, New Jacobi elliptic function solutions, solitons and other solutions for the (2 + 1)-dimensional nonlinear electrical transmission line equation, The European Physıcal Journal Plus, 133(214) (2018), 1-7.
  • [19] M.T. Gulluoglu, New Complex Solutions to the Nonlinear Electrical Transmission Line Model, Open Phys., 17 (2019), 823-830.
  • [20] M.S. Osman, H. Rezazadeh, M. Eslami, A. Neirameh and M. Mirzazadeh, Analytical study of solitons to Benjamin-Bona-Mahony-Peregrine Equation with power law nonlinearity by using three methods, U.P.B. Sci. Bull., Series A, 80 (2018), 1-12.
  • [21] C.M. Khalique, Solutions and conservation laws of Benjamin–Bona–Mahony–Peregrine equation with power-law and dual power-law nonlinearities, Pramana Journal of Physics, 80(3) (2013), 413-427.
  • [22] H. Aminikhah, B.P. Ziabary and H. Rezazadeh, Exact traveling wave solutions of partial differential equations with power law nonlinearity, Nonlinear Engineering, 4(3) (2015), 181-188.
Year 2022, Volume: 10 Issue: 2, 301 - 312, 31.10.2022

Abstract

References

  • [1] A.M. Wazwaz, The Hirota’s direct method and the tanh–coth method for multiplesoliton solutions of the Sawada–Kotera–Ito seventh-order equation, Applied Mathematics and Computation, 199 (2008), 133-138.
  • [2] F. Pelap, J. Kamga, A. Fomethe, A. Kenfack and M. Fave, Wave dynamics in a modified quintic complex Ginzburg-Landau system, Phys. Lett. A, 373 (2009), 1015-1018.
  • [3] Y. Pandir and A. Ekin, Dynamics of combined soliton solutions of unstable nonlinear Schrodinger equation with new version of the trial equation method, Chinese Journal of Physics, 67 (2020), 534-543.
  • [4] S.T.R. Rizvi, K. Ali, A. Sardar, M. Younis and A. Bekir, Symbolic computation and abundant travelling wave solutions to KdV-mKdV equation, Pramana, 88(1) (2017), 1-6.
  • [5] A. Irshad and S.T. Mohyud-Din, Tanh-Coth Method for Nonlinear Differantial Equations, Studies in Nonlinear Sciences, 3(1) (2012), 24-48.
  • [6] H.F. Ismael, A. Seadawy and H. Bulut, Construction of breather solutions and N-soliton for the higher order dimensional Caudrey– Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns, International Journal of Nonlinear Sciences and Numerical Simulation, (2021), 000010151520200169.
  • [7] H.F. Ismael and H. Bulut, Nonlinear dynamics of (2+1)-dimensional Bogoyavlenskii–Schieff equation arising in plasma physics, Mathematical Methods in the Aapplied Sciences, 44(13) (2021), 10321-10330.
  • [8] H.F. Ismael, A. Seadawy and H. Bulut, Rational solutions, and the interaction solutions to the (2+1)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation, International Journal of Computer Mathematics, 98(12) (2021), 2369-2377.
  • [9] H.F. Ismael, S.S. Atas, H. Bulut and M.S. Osman, Analytical solutions to the M-derivative resonant Davey–Stewartson equations, Modern Physics Letters B, 35(30) (2021), 2150455.
  • [10] Y. Pandir, Y. Gurefe, U. Kadak and E. Misirli, Classification of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstract and Applied Analysis, 2012 (2012), 1-16.
  • [11] H. Bulut, Y. Pandir and S. Tuluce Demiray, Exact Solutions of Nonlinear Schrodinger’s Equation with Dual Power-Law Nonlinearity by Extended Trial Equation Method, Waves in Random and Complex Media, 24(4) (2014), 439-451.
  • [12] S. Tuluce Demiray and H. Bulut, Some exact solutions of generalized Zakharov system, Waves in Random and Complex Media, 25(1) (2015), 75-90.
  • [13] S. Tuluce Demiray, Y. Pandir and H. Bulut, New Solitary Waves Solutions of Maccari System, Ocean Engineering, 103 (2015), 153-159.
  • [14] S. Tuluce Demiray, Y. Pandir and H. Bulut, New Soliton Solutions for Sasa-Satsuma Equation, Waves in Random and Complex Media, 25(3) (2015), 417-428.
  • [15] W. Kang-Jia and W. Guo-Dong, Periodic solution of the (2+1)-dimensional nonlinear electrical transmission line equation via variational method, Results in Physics, 20 (2021), 1-2.
  • [16] M.A. Kayum, S. Ara, H.K. Barman and M.A. Akbar, Soliton solutions to voltage analysis in nonlinear electrical transmission lines and electric signals in telegraph lines, Results in Physics, 18 (2020), 1-10.
  • [17] E. Tala-Tebue, D.C. Tsobgni-Fozap, A. Kenfack-Jiotsa and T.C. Kofane, Envelope periodic solutions for a discrete network with the Jacobi elliptic functions and the alternative (G0=G)-expansion method including the generalized Riccati equation, The European Physıcal Journal Plus, 129(136) (2014), 1-10.
  • [18] E. Tala-Tebue and E.M.E. Zayed, New Jacobi elliptic function solutions, solitons and other solutions for the (2 + 1)-dimensional nonlinear electrical transmission line equation, The European Physıcal Journal Plus, 133(214) (2018), 1-7.
  • [19] M.T. Gulluoglu, New Complex Solutions to the Nonlinear Electrical Transmission Line Model, Open Phys., 17 (2019), 823-830.
  • [20] M.S. Osman, H. Rezazadeh, M. Eslami, A. Neirameh and M. Mirzazadeh, Analytical study of solitons to Benjamin-Bona-Mahony-Peregrine Equation with power law nonlinearity by using three methods, U.P.B. Sci. Bull., Series A, 80 (2018), 1-12.
  • [21] C.M. Khalique, Solutions and conservation laws of Benjamin–Bona–Mahony–Peregrine equation with power-law and dual power-law nonlinearities, Pramana Journal of Physics, 80(3) (2013), 413-427.
  • [22] H. Aminikhah, B.P. Ziabary and H. Rezazadeh, Exact traveling wave solutions of partial differential equations with power law nonlinearity, Nonlinear Engineering, 4(3) (2015), 181-188.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Şeyma Tülüce Demiray

Merve Davarcı Yalçın This is me 0000-0002-4862-7836

Publication Date October 31, 2022
Submission Date January 24, 2022
Acceptance Date February 17, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Tülüce Demiray, Ş., & Davarcı Yalçın, M. (2022). Traveling Wave Solutions of Some Nonlinear Partial Equations. Konuralp Journal of Mathematics, 10(2), 301-312.
AMA Tülüce Demiray Ş, Davarcı Yalçın M. Traveling Wave Solutions of Some Nonlinear Partial Equations. Konuralp J. Math. October 2022;10(2):301-312.
Chicago Tülüce Demiray, Şeyma, and Merve Davarcı Yalçın. “Traveling Wave Solutions of Some Nonlinear Partial Equations”. Konuralp Journal of Mathematics 10, no. 2 (October 2022): 301-12.
EndNote Tülüce Demiray Ş, Davarcı Yalçın M (October 1, 2022) Traveling Wave Solutions of Some Nonlinear Partial Equations. Konuralp Journal of Mathematics 10 2 301–312.
IEEE Ş. Tülüce Demiray and M. Davarcı Yalçın, “Traveling Wave Solutions of Some Nonlinear Partial Equations”, Konuralp J. Math., vol. 10, no. 2, pp. 301–312, 2022.
ISNAD Tülüce Demiray, Şeyma - Davarcı Yalçın, Merve. “Traveling Wave Solutions of Some Nonlinear Partial Equations”. Konuralp Journal of Mathematics 10/2 (October 2022), 301-312.
JAMA Tülüce Demiray Ş, Davarcı Yalçın M. Traveling Wave Solutions of Some Nonlinear Partial Equations. Konuralp J. Math. 2022;10:301–312.
MLA Tülüce Demiray, Şeyma and Merve Davarcı Yalçın. “Traveling Wave Solutions of Some Nonlinear Partial Equations”. Konuralp Journal of Mathematics, vol. 10, no. 2, 2022, pp. 301-12.
Vancouver Tülüce Demiray Ş, Davarcı Yalçın M. Traveling Wave Solutions of Some Nonlinear Partial Equations. Konuralp J. Math. 2022;10(2):301-12.
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