Geodesic
Intermediate systems and higher-order differential constraints
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 5, pp. 550-560

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A method for constructing solutions of nonlinear partial differential equations with two independent variables is proposed. The method is based on the search for so-called intermediate systems, each solution of which satisfies the initial equation. The main attention is paid to a second order nonlinear wave equation. We give examples of intermediate systems and corresponding solutions.
Keywords: differential constraints, defining equations, invariant manifolds. 
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     author = {Oleg V. Kaptsov},
     title = {Intermediate systems and higher-order differential constraints},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {550--560},
     publisher = {mathdoc},
     volume = {11},
     number = {5},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_5_a1/}
}
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Oleg V. Kaptsov. Intermediate systems and higher-order differential constraints. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 5, pp. 550-560. http://geodesic.mathdoc.fr/item/JSFU_2018_11_5_a1/