New non-invertible mappings and general solutions of linear wave equations with variable wave speeds

TL;DR

This paper introduces new non-invertible mappings for linear wave equations with variable wave speeds, enabling the derivation of their general solutions through symmetry-based methods.

Contribution

It presents novel non-invertible equivalence mappings that transform variable wave speed equations into other wave equations, including constant wave speed cases, expanding solution techniques.

Findings

Derived new non-invertible mappings for wave equations

Obtained general solutions for variable wave speed equations

Extended symmetry methods to non-invertible transformations

Abstract

We show how the symmetry-based method can be used to obtain new non-invertible equivalence mappings of linear wave equations with variable wave speeds $c(x,t)$ to linear wave equations with different variable wave speeds. Moreover, we present new non-invertible mappings of linear wave equations with variable wave speeds $c(x,t)$ to a linear wave equation with a constant wave speed. Consequently, the general solutions of these linear wave equations with variable wave speeds $c(x,t)$ are obtained.