Solutions of Non-Integrable Equations by the Hirota Direct Method

TL;DR

This paper demonstrates the application of the Hirota direct method to certain non-integrable equations, specifically extended KP and Boussinesq equations, providing explicit solutions for these extended models.

Contribution

It extends the Hirota method to non-integrable equations, offering new solutions for modified KP and Boussinesq equations.

Findings

Successfully applied Hirota method to non-integrable equations

Derived explicit solutions for extended KP and Boussinesq equations

Shows potential for solving other non-integrable nonlinear equations

Abstract

We show that we can also apply the Hirota method to some non-integrable equations. For this purpose, we consider the extensions of the Kadomtsev-Petviashvili (KP) and the Boussinesq (Bo) equations. We present several solutions of these equations.