New exact solutions of a nonlinear long–short wave interaction system

This paper presents new exact solutions of a nonlinear long–short wave interaction system using two different methods named, the new Jacobi elliptic function expansion (NJEFE) method and the modified Kudryashov method (KM). Different types of solutions are obtained including, hyperbolic and Jacobi elliptic functions. The approaches used produce various dynamical wave structures of soliton solutions in evolutionary dynamical structures of solitary wave solutions. The useful parameter selections are permitted in order to provide a solution. To better comprehend the physical phenomena of these dynamical models that arise in mathematical physics, the physical behavior of these solutions is presented. The methods are efficient and can be used to produce novel solutions for different types of nonlinear partial differential equations.