On classification of higher-order integrable nonlinear partial differential equations

TL;DR

This paper classifies higher-order integrable nonlinear PDEs and investigates solitonic solutions using the Hirota method, advancing understanding of complex nonlinear systems.

Contribution

It provides a classification scheme for higher-order integrable PDEs and applies the Hirota method to find solitonic solutions, offering new insights into nonlinear integrable systems.

Findings

Classification of higher-order integrable PDEs

Existence of solitonic solutions demonstrated

Application of Hirota method to complex systems

Abstract

We investigate existence of solitonic solutions for higher-order partial differential equations with polynomial nonlinearities. Using the Hirota method we obtain classification for higher-order integrable systems of equations.