On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed c<sup>2</sup> = x

Dobrokhotov S.Y.; Minenkov D.S.; Medvedev S.B.

doi:10.1134/S0001434613050064

Инд. авторы:	Dobrokhotov S.Y., Minenkov D.S., Medvedev S.B.
Заглавие:	On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed c² = x
Библ. ссылка:	Dobrokhotov S.Y., Minenkov D.S., Medvedev S.B. On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed c² = x // Mathematical Notes. - 2013. - Vol.93. - Iss. 5-6. - P.704-714. - ISSN 0001-4346. - EISSN 1573-8876.
Внешние системы:	DOI: 10.1134/S0001434613050064; РИНЦ: 20438790; WoS: 000321274300006;
Реферат:	eng: We obtain point transformations for three one-dimensional systems: shallow-water equations on a flat and a sloping bottom and the system of linear equations obtained by formal linearization of shallow-water equations on a sloping bottom. The passage of these systems to the Carrier-Greenspan parametrization is also obtained. For linear shallow-water equations on a sloping bottom, we obtain the solution in the form of a traveling wave with variable velocity. We establish the relationship between the resulting solution and the solution of the two-dimensional wave equation.
Издано:	2013
Физ. характеристика:	с.704-714