English

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

Analysis of PDEs 2025-07-22 v1

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)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)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)c(x,t) are obtained.

Keywords

Cite

@article{arxiv.2507.14522,
  title  = {New non-invertible mappings and general solutions of linear wave equations with variable wave speeds},
  author = {Rafael de la Rosa and George W. Bluman},
  journal= {arXiv preprint arXiv:2507.14522},
  year   = {2025}
}