This article is cited in 2 papers

Steady oscillations in a continuously inhomogeneous medium described by the Ovsyannikov equation

Yu. A. Chirkunov<sup>ab

a</sup> Novosibirsk State Technical University, Novosibirsk
^b Institute of Computational Technologies, SB RAS, Novosibirsk

Abstract: Using group analysis methods, for the Ovsyannikov equation with maximal symmetry which describes steady oscillations in a continuously inhomogeneous medium we obtain an exact solution to the boundary value problems for some regions (a generalized Poisson formula), which in particular can serve as test solutions for simulating steady oscillations in continuously inhomogeneous media. We find operators acting on the set of solutions in a one-parameter family of these equations.

Keywords: Ovsyannikov equation, maximal symmetry, steady oscillations in continuously inhomogeneous medium, intertwining operators, generalized Poisson formula.

UDC: 517.956

Received: 13.05.2009

 English version: Journal of Applied and Industrial Mathematics, 2011, 5:3, 313–321

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