Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Admitted Conservation Laws

TL;DR

This paper introduces an algorithmic approach using conservation law multipliers to find invertible mappings that linearize nonlinear PDEs, providing a systematic alternative to symmetry-based methods.

Contribution

The paper presents a new method leveraging conservation law multipliers to determine and construct invertible linearizations of nonlinear PDEs, expanding beyond symmetry-based techniques.

Findings

The method provides necessary and sufficient conditions for linearization.

It successfully constructs invertible mappings in example cases.

It offers a systematic alternative to symmetry-based linearization approaches.

Abstract

An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.