Intermediate systems and higher-order differential constraints

Oleg V. Kaptsov

Institute of Computational Modelling SD RAS, Academgorodok, 50/44, Krasnoyarsk, 660036, Russia

Abstract: 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.

UDC: 519.21

Received: 10.03.2018
Received in revised form: 20.04.2018
Accepted: 06.06.2018

Language: English

DOI: 10.17516/1997-1397-2018-11-5-550-560

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