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arXiv · 2507.14522

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

Rafael de la Rosa·George W. Bluman
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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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Rafael de la Rosa, George W. Bluman. 2025-07-19. New non-invertible mappings and general solutions of linear wave equations with variable wave speeds. https://arxiv.org/abs/2507.14522

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