Abstract
We develop a generalized conditional symmetry approach for the functional separation of variables in a nonlinear wave equation with a nonlinear wave speed. We use it to obtain a number of new (1+1)-dimensional nonlinear wave equations with variable wave speeds admitting a functionally separable solution. As a consequence, we obtain exact solutions of the resulting equations.
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Estévez, P.G., Qu, C.Z. Separation of Variables in a Nonlinear Wave Equation with a Variable Wave Speed. Theoretical and Mathematical Physics 133, 1490–1497 (2002). https://doi.org/10.1023/A:1021190509331
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DOI: https://doi.org/10.1023/A:1021190509331