Solitary wave and other solutions for nonlinear heat equations

TL;DR

This paper presents new exact solutions for nonlinear heat equations, including solitary waves and generalized Fisher equations with arbitrary propagation velocities, expanding the understanding of nonlinear heat phenomena.

Contribution

It introduces an extended class of nonlinear heat equations with solitary wave solutions and generalizes the Fisher equation to include solutions with arbitrary fixed velocities.

Findings

New exact solitary wave solutions for nonlinear heat equations

Generalized Fisher equation with arbitrary propagation velocity

Expanded class of nonlinear heat equations admitting solitary waves

Abstract

New exact solutions for the heat equation with a polynomial non-linearity and for the Fisher equation are found. An extended class of non-linear heat equations admitting solitary wave solutions is found. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.