Geodesic
Separation of Variables in a~Nonlinear Wave Equation with a~Variable Wave Speed
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 202-210

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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.
Keywords: Lie symmetries, generalized symmetries, nonlinear equations.
Mots-clés : diffusion equations 
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     author = {P. G. Estevez and C. Qu},
     title = {Separation of {Variables} in {a~Nonlinear} {Wave} {Equation} with {a~Variable} {Wave} {Speed}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {202--210},
     publisher = {mathdoc},
     volume = {133},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a5/}
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P. G. Estevez; C. Qu. Separation of Variables in a~Nonlinear Wave Equation with a~Variable Wave Speed. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 202-210. http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a5/