Another look at the solution of the equations; the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation.
DOI:
https://doi.org/10.24054/bistua.v22i1.2526Keywords:
Traveling wave solutions, Partial differential equations, Mathematical physicsAbstract
In [1] the authors present an analytical method for solving nonlinear evolution equations, and apply it to find ”new solutions”, of the equations mBBM and mKdV. In this note we prove that these solutions can be found from the general solution and that the method exposed in [1], is not as effective as claimed.
Downloads
References
C.A. Gómez, Harun-Or Roshid, M. Inc, L. Akinyemi, and H. Rezaza-deh. (2022). On soliton solutions for perturbed Fokas- Lenells eqution.Optical and Quantum Electronics, vol. 54, no. 370, 1–10.
K. S. A. Ghafri and E. V. Krishrar. (2020). Arjar Biswas, Chirped opticalsoliton perturbation of Fokas-Lenells equation with full nonlinearity.Advanced in Differential Equations. vol. 2020, 191.
A. Bansal, A. H. Kara, A. Biswas, S. P. Moshokoa, and M. Belic. (2018).Optical soliton perturbation, group invariants and conservation laws ofperturbed Fokas–Lenells equation.Chaos, Solitons and Fractals, vol.114, 275–280.
K. K. Ali, M. S. Osman, and M. Abdel Aty. (2020). New optical soli-tary wave solutions of Fokas-Lenells equation in optical :ber via Sine-Gordon expansion method.Alexandria Engineering Journal, vol. 59, no.3, 1191–1196.
Y. Yildirim, A. Biswas, M. Asma et al.(2018). Chirp-free bright opticalsoliton perturbation with Chen–Lee–Liu equation by traveling wavehypothesis and semi-inverse variational principle.Optik, vol. 172, no.172, 772–776.
E. M. E. Zayed and K. A. E. Alurr. (2016). New extended auxiliaryequation method and its applications to nonlinear Schrodinger-typeequations.Optik, vol. 127, no. 20, 9131–9151, 2016.
A. M. Wazwaz.(2007). The tanh-coth method for solitons and kinksolutions for nonlinear parabolic equations.Applied Mathematics andComputation, vol. 188, no. 2, 1467–1475.
S. B. G. Karakoc, K. K. Ali, and M. S. Mehanna. (2023). Exact travelingwave solutions of the schamel-KdV equation with two different methods.Universal Journal of Mathematics and Applications, vol. 6, no. 2, 65–75.
Islam MS, Khan K, Akbar MA, Mastroberardino A. (2014 ). A noteon improved F-expansion method combined with Riccati equation ap-plied to nonlinear evolution equations.R.Soc. open sci. 1: 140038. 1-13.https://royalsocietypublishing.org/doi/epdf/10.1098/rsos.140038
Edwards, Penney. (1986). Ecuaciones diferenciales con aplicaciones México.Prentice-Hall.
Whittaker, E.T, Watson.G.V. (2008). A course of Modern Analy-sis.fourth edition. Cambridge. Cambridge University Press.http://dx.doi.org/10.1007/978-94-010-0273-8-11.
Downloads
Published
Versions
- 2024-06-21 (2)
- 2024-06-21 (1)
Issue
Section
License
Copyright (c) 2024 Juan Carlos López Carreño, Rosalba Mendoza Suárez, Jairo Alonso Mendoza Suárez
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
