Инд. авторы:	Chirkunov Y.A., Medvedev S.B., Dobrokhotov S.Y., Minenkov D.S.
Заглавие:	Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms
Библ. ссылка:	Chirkunov Y.A., Medvedev S.B., Dobrokhotov S.Y., Minenkov D.S. Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms // Theoretical and Mathematical Physics. - 2014. - Vol.178. - Iss. 3. - P.278-298. - ISSN 0040-5779. - EISSN 1573-9333.
Внешние системы:	DOI: 10.1007/s11232-014-0143-4; РИНЦ: 21872629; WoS: 000334254700002;
Реферат:	eng: We establish an equivalence of two systems of equations of one-dimensional shallow water models describing the propagation of surface waves over even and sloping bottoms. For each of these systems, we obtain formulas for the general form of their nondegenerate solutions, which are expressible in terms of solutions of the Darboux equation. The invariant solutions of the Darboux equation that we find are simplest representatives of its essentially different exact solutions (those not related by invertible point transformations). They depend on 21 arbitrary real constants; after "proliferation" formulas derived by methods of group theory analysis are applied, they generate a 27-parameter family of essentially different exact solutions. Subsequently using the derived infinitesimal "proliferation" formulas for the solutions in this family generates a denumerable set of exact solutions, whose linear span constitutes an infinite-dimensional vector space of solutions of the Darboux equation. This vector space of solutions of the Darboux equation and the general formulas for nondegenerate solutions of systems of shallow water equations with even and sloping bottoms give an infinite set of their solutions. The "proliferation" formulas for these systems determine their additional nondegenerate solutions. We also find all degenerate solutions of these systems and thus construct a database of an infinite set of exact solutions of systems of equations of the one-dimensional nonlinear shallow water model with even and sloping bottoms.
Ключевые слова:	symmetry group; invariant solution; exact solution; Euler-Poisson-Darboux equation; shallow water equation;
Издано:	2014
Физ. характеристика:	с.278-298