Moving Boundary Problems for a Cuspon Equation and Reciprocal Associates: Exact Solution via Painleve' Symmetry Reduction

TL;DR

This paper presents exact solutions for moving boundary problems related to cuspon equations and reciprocal solitonic equations using Painleve' II symmetry reduction.

Contribution

It introduces a novel approach to solving Stefan-type boundary problems for cuspon and reciprocal equations through Painleve' II symmetry reduction.

Findings

Exact solutions for moving boundary problems are obtained.

The method applies to both established cuspon equations and new reciprocal solitonic equations.

The approach demonstrates the utility of Painleve' II symmetry in nonlinear boundary problems.

Abstract

Here classes of moving boundary problems of Stefan-type for both an established non-linear evolution equation of cuspon theory and novel reciprocally linked solitonic equations are shown to be solvable via Painleve' II symmetry reduction.