KINK WAVE SOLUTIONS FOR THE (1+1)-DIMENSIONAL NONLINEAR EVOLUTION EQUATION BY THE SE METHOD WITH THE BERNOULLI EQUATION
Keywords:
King waves;, the simple method with the Bernoulli equation;, the (1+1)-dimensional Phi-Four equation;Abstract
The primary objective of this research is to fully solve the (1+1)-dimensional Phi-Four equation and the (1+1)-dimensional modified Korteweg-De Vries equation, which are the nonlinear partial differential equations, into the nonlinear ordinary differential equations by using the traveling wave transformation and solve these solutions with the simple method (SE) with the Bernoulli equation. The solutions are shown by the exponential functions, which can be transformed into kink waves. Their graphical representations are three-dimensional graphs, and contour graphs are shown using suitable parameter values. Furthermore, the findings confirmed that the techniques employed in this investigation were effective mathematical instruments for locating precise wave solutions to nonlinear models.
References
Phoosree, S., Khongnual, N., Sanjun, J., Kammanee, A., & Thadee, W. (2024). Riccati sub-equation method for solving fractional flood wave equation and fractional plasma physics equation. Partial Differential Equations in Applied Mathematics, 10, 100672.
Nofal, T. A. (2016). Simple equation method for nonlinear partial differential equations and its applications. Journal of the Egyptian Mathematical Society, 24(2), 204-209.
Sanjun, J. and Chankaew, A. (2022). Wave solutions of the DMBBM equation and the cKG equation using the simple equation method. Frontiers in Applied Mathematics and Statistics, 8(1), 952668.
Iqbal, M. S., Seadawy, A. R., Baber, M. Z., & Qasim, M. (2022). Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions. Chaos, Solitons & Fractals, 164, 112600.
Kumar, A. and Pankaj, R. D. (2015). Tanh–coth scheme for traveling wave solutions for Nonlinear Wave Interaction model. Journal of the Egyptian Mathematical Society, 23(2), 282-285.
Raslan, K. R., EL-Danaf, T. S. and Ali, K. K. (2017). New exact solution of coupled general equal width wave equation using sine-cosine function method. Journal of the Egyptian Mathematical Society, 25(3), 350-354.
Djennadi, S., Shawagfeh, N., & Arqub, O. A. (2021). A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation. Partial Differential Equations in Applied Mathematics, 4, 100164.
Momani, S., Abu Arqub, O., & Maayah, B. (2020). Piecewise optimal fractional reproducing kernel solution and convergence analysis for the Atangana–Baleanu–Caputo model of the Lienard’s equation. Fractals, 28(08), 2040007.
Sanjun, J., Aphaisawat, W. and Korkiatsakul, T. (2024). Effect of wave solution on Landau-Ginzburg-Higgs equation and modified KdV-Zakharov equation by the Riccati-Bernoulli sub-ODE method. Journal of Applied Science and Emerging Technology, 23(1), e253520-e253520.
Behera, S., & Aljahdaly, N. H. (2023). Nonlinear evolution equations and their traveling wave solutions in fluid media by modified analytical method. Pramana, 97(3), 130.
Abdel-Gawad, H. I., Tantawy, M. and Abdelwahab, A. M. (2022). A new technique for solving Burgers-Kadomtsev-Petviashvili equation with an external source. Suppression of wave breaking and shock wave. Alexandria Engineering Journal, 69(1), 167-176,
Deng, X., Zhao, M. and Li, X. (2009). Travelling wave solutions for a nonlinear variant of the PHI-four equation. Mathematical and Computer Modelling, 49(3-4), 617-622.
Abdelrahman, M. A. E. and Sohaly, M. A. (2017). Solitary waves for the modified Korteweg-de Vries equation in deterministic case and random case. J. Phys. Math, 8(1), 2090-0902.
Phoosree, S. and Thadee, W. (2022). Wave effects of the fractional shallow water equation and the fractional optical fiber equation. Frontiers in Applied Mathematics and Statistics, 8, 900369.
Chankaew, A., Phoosree, S. and Sanjun, J. (2023). Exact solutions of the fractional Landau-Ginzburg-Higgs equation and the (3+ 1)-dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation using the simple equation method. Journal of Applied Science and Emerging Technology, 22(3), e253149-e253149.
Phoosree, S., Kammanee, A., Kangkasuwan, T. and Thadee, W. (2024). Novel fractional solutions and singular kink effect of some fluid mechanics equation and long wave propagation equation via simple equation method. ESS Open Archive eprints, 373, 37375267.
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