Geodesic
Families of exact solutions for linear and nonlinear wave equations with a~variable speed of sound and their use in solving initial boundary value problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 41-50

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We propose a procedure for multiplying solutions of linear and nonlinear one-dimensional wave equations, where the speed of sound can be an arbitrary function of one variable. We obtain exact solutions. We show that the functional series comprising these solutions can be used to solve initial boundary value problems. For this, we introduce a special scalar product.
Mots-clés : exact solution
Keywords: wave equation, Bäcklund transformation. 
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     author = {E. V. Trifonov},
     title = {Families of exact solutions for linear and nonlinear wave equations with a~variable speed of sound and their use in solving initial boundary value problems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {41--50},
     publisher = {mathdoc},
     volume = {192},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a2/}
}
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E. V. Trifonov. Families of exact solutions for linear and nonlinear wave equations with a~variable speed of sound and their use in solving initial boundary value problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 41-50. http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a2/