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

2025/07/19 by de la Rosa, Rafael, Bluman, George W.
#35B06 #35C05 #35L05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.14522

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.

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