Application of new Kudryashov method to various nonlinear partial differential equations

The purpose of this work is to seek various innovative exact solutions using the new Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This technique obtains novel exact solutions of soliton types. Moreover, several 3D and 2D plots of the higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are demonstrated by considering the relevant values of the aforementioned parameters to exhibit the nonlinear wave structures more adequately. The new Kudryashov technique is an effective, and simple technique that provides new generalized solitonic wave profiles. It is anticipated that these novel solutions will enable a thorough understanding of the development and dynamic nature of such models.

Automated summary

The purpose of this work is to find innovative exact solutions for nonlinear partial differential equations using the new Kudryashov approach. The technique provides novel exact solutions of soliton types. 3D and 2D plots of higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are shown to better understand the nonlinear wave structures. The new Kudryashov technique is effective and simple, providing new generalized solitonic wave profiles that enhance the understanding of the development and dynamic nature of such models.