Solitary Wave Solutions for the Shallow Water Wave Equations and the Generalized Klein-Gordon Equation Using Exp(-ϕ(η) )-Expansion Method
Md. Mamunur Rashid, Whida Khatun
Journal of Advances in Mathematics and Computer Science · pp. 72–86 · Published 29 Jun 2020
10.9734/jamcs/2020/v35i430272Abstract
In this article, we investigate the exact and solitary wave solutions for the shallow water wave equations and the generalized Klein-Gordon equation using the exp -expansion method. A wave transformation is applied to convert the problem into the form of an ordinary differential equation. By using this method, we found the explicit solitary wave solutions in terms of the hyperbolic functions, trigonometric functions, exponential functions and rational functions. The extracted solution plays a significant role in many physical phenomena such as electromagnetic waves, nonlinear lattice waves, ion sound waves in plasma, nuclear physics, shallow water waves and so on. It is noted that the method is reliable, straightforward and an effective mathematical tool for analytic treatment of nonlinear systems of partial differential equation in mathematical physics and engineering.
Cited by 9
Snehalata Nasipuri, Prasanta Chatterjee · Pramana · 2025
Kang-Jia Wang, Jing-Hua Liu, Jun Wu · Optik · 2022
Kang-jia Wang, Jing-Hua Liu · Journal of Ocean Engineering and Science · 2023
Kang-Jia Wang · Modern Physics Letters B · 2023
KANG-JIA WANG, PENG XU, FENG SHI · Fractals · 2023
KANG-JIA WANG, FENG SHI · Fractals · 2024
KANG-JIA WANG, GUO-DONG WANG, FENG SHI · Fractals · 2022
Kang-Jia Wang, Jing Si · The European Physical Journal Plus · 2023
KANG-JIA WANG, SHUAI LI · Fractals · 2024
Related research
- Compacton, Peakon and Solitary Wave Solutions of the Osmosis K (3,2) Equation — shares topic coverage
- Traveling Wave Solutions for a Coupled KdV Equations — shares topic coverage
- Solutions of Schrödinger and Klein-Gordon Equations with Hulthen Plus Inversely Quadratic Exponential Mie-Type Potential — shares topic coverage
- Bound State Solutions of the Klein-Gordon Equation with Manning-Rosen Plus Yukawa Potential Using Pekeris-Like Approximation of the Coulomb Term and Parametric Nikiforov-Uvarov — shares topic coverage
- Solutions of Klein-Gordon Equation by the Laplace Decomposition Method and Modified Laplace Decomposition Method — shares topic coverage
Article metrics
Real usage data collected on this platform.
7
Page views
0
PDF downloads
1
Outbound clicks
9
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.