Geodesic
Special classes of solutions to the equations of horizontal-displacement fluid motion
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 3, pp. 50-57

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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. 
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     title = {Special classes of solutions to the equations of horizontal-displacement fluid motion},
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P. V. Kovtunenko; A. A. Chesnokov. Special classes of solutions to the equations of horizontal-displacement fluid motion. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 3, pp. 50-57. http://geodesic.mathdoc.fr/item/SJIM_2011_14_3_a5/