Function expansion methods for solving autonomous nonlinear partial differential equations

TL;DR

This paper introduces new function expansion algorithms for analytically solving nonlinear polynomial PDEs, unifying existing methods and demonstrating effectiveness on physics-related equations.

Contribution

It develops unified algorithms for solving nonlinear PDEs using one-, two-, and three-function expansion methods, encompassing and extending existing approaches.

Findings

Methods successfully solve nonlinear PDEs in physics

Unified framework recovers most existing expansion methods

Effective for equations with constant coefficients

Abstract

In this paper, we propose some algorithms for analytical solution construction to nonlinear polynomial partial differential equations with constant function coefficients. These schemes are based on one-(single), two- (double) or three- (triple) function expansion methods. Most of the existing expansion function methods are well recovered from the mentioned schemes. The effectiveness of these methods has been tested on some nonlinear partial differential equations (NLPDEs) describing important phenomena in physics.