Classes of new analytical soliton solutions to some nonlinear evolution equations

Undoubtedly, all applied sciences are closely corresponding to differential equations, especially partial differential equations. This contribution aims to examine the efficiency of a modified version of the generalized exponential rational function method in solving some well-known nonlinear evolution equations. The investigated models in this article include the Zakharov–Kuznetsov, the cubic Boussinesq, and the modified regularized long-wave equation. In the structure of these solutions, various familiar elementary functions, including exponential, trigonometric, and hyperbolic functions are used. This important feature makes it easy to use these solutions in real applications. Numerical behaviors corresponding to the obtained solutions have been demonstrated through some three-dimensional diagrams in the article. This technique can be also adopted in determining wave soliton solution to other equations with partial derivatives. •Analytical solutions to several nonlinear evolution equations are obtained.•We utilized a modified version of the generalized exponential rational function method.•The acquired solutions are new and have not been reported before.•The employed methodology is also adaptable in solving other nonlinear equations.