Abundant new analytical and approximate solutions to the generalized Schamel equation

Abstract

An exact solution of partial differential equations provides a lot of information for a model. Since obtaining such answers is generally very difficult or in some cases impossible, having powerful analytical methods in determining them seems very necessary. Unlike numerical methods, these methods have fewer constraints such as stability, convergence, and approximation error. This paper aims to consider the generalized Schamel equation which arises in the modeling of some problems in plasma physics. Fortunately, by applying a new analytical method, a large number of exact solutions to the model are obtained. The structure used in the solutions specified in this method uses Jacobi elliptic functions. In another part of the paper, an effective numerical method, namely the reproducing kernel method is used to approximate the solutions of the equation. Numerical simulations of some acquired exact and approximate solutions are also included. It seems that the employed methods can be considered as effective, powerful, and straightforward methods of studying equations. The methods can also be utilized to investigate other partial differential equations.