Abstract
Abstract In this article, the system for the long–short-wave interaction (LS) system is considered. In order to construct some new traveling wave solutions, He’s semi-inverse method is implemented. These solutions may be applicable for some physical environments, such as physics and fluid mechanics. These new solutions show that the proposed method is easy to apply and the proposed technique is a very powerful tool to solve many other nonlinear partial differential equations in applied science.
Highlights
Nonlinear partial differential equations (NLPDEs) are encountered in many fields of applied science, e.g., optics, plasma physics solid state physics, fluid mechanics and chemical engineering [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
By developing a specific transformation, the NLPDEs are converted into an ordinary differential equation (ODE)
This study shows that the proposed method is reliable in handling NPDEs to establish a variety of exact solutions
Summary
Nonlinear partial differential equations (NLPDEs) are encountered in many fields of applied science, e.g., optics, plasma physics solid state physics, fluid mechanics and chemical engineering [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. By developing a specific transformation, the NLPDEs are converted into an ordinary differential equation (ODE). Expanding the methods to the search of NLPDEs for traveling wave solutions seems to be interesting and helpful to the mathematicians, physicists and engineers. We employee He’s semi-inverse technique to gain the solutions for the long–short-wave interaction (LS) system. Most other papers concerning He’s semi-inverse technique give only one family. This article is organized as follows: in Section 2, we recall He’s semi-inverse technique.
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