Special classes of solutions to the equations of horizontal-displacement fluid motion

P. V. Kovtunenko^ab, A. A. Chesnokov<sup>ab

a</sup> Lavrent'ev Institute of Hydrodynamics SB RAS, Novosibirsk, RUSSIA
^b Novosibirsk State University, Novosibirsk, RUSSIA

Abstract: We construct a special class of solutions to nonlinear integrodifferential equations describing horizontal-displacement motion of ideal fluid in an open channel in the shallow water approximation. This class of solutions is characterized by a linear relation among Riemann integral invariants and is determined by a hyperbolic system of two differential equations with two parameters. In the class of traveling waves we construct exact solutions, including arbitrary functions, to the equations of motion continuously adjacent to a given displacement flow.

UDC: 517.958+532.591

Received: 29.10.2010

Bibliographic databases:

•