New Traveling Wave Solutions to the Simplified Modified Camassa–Holm Equation and the Landau-Ginsburg-Higgs Equation

Authors

  • Md Sagib Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur 5200, Bangladesh.
  • Bishnu Pada Ghosh Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh
  • Nepal Chandra Roy Department of Mathematics, Dhaka University, Dhaka 1000, Bangladesh

DOI:

https://doi.org/10.3329/dujs.v72i1.71029

Keywords:

Extended (G^'/G)-expansion method; Camassa-Holm equation; Landau-Ginzburg-Higgs equation; Traveling wave solutions; Soliton

Abstract

Researchers are interested in the (1+1)-dimensional Camassa-Holm and Landau-Ginzburg-Higgs equations as they allow for the study of unidirectional wave propagation in shallow waters with a flat seabed, as well as nonlinear media exhibiting dispersion systems and superconductivity. This work has effectively developed exact wave solutions to the stated models, which may have significant consequences for characterising the nonlinear dynamical behaviour related to the phenomena. The extended -expansion technique is employed to procure a diverse array of progressive wave solutions characterized by hyperbolic, trigonometric, and rational functions. The solutions are shown as 3D profiles with a variety of shapes, including kink, singular kink, periodic, singular periodic, etc. The physical significance of the solutions is discussed by these plots, and the approach used in this study is considered efficient and capable of finding analytical solutions for the nonlinear models.

Dhaka Univ. J. Sci. 72(1): 7-13, 2024 (January)

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Published

2024-03-25

How to Cite

Sagib, M., Ghosh, B. P., & Roy, N. C. . (2024). New Traveling Wave Solutions to the Simplified Modified Camassa–Holm Equation and the Landau-Ginsburg-Higgs Equation. Dhaka University Journal of Science, 72(1), 7–13. https://doi.org/10.3329/dujs.v72i1.71029

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