International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 557-562
doi:10.1155/S016117128700067X
The shallow water equations: Conservation laws and symplectic geometry
Yilmaz Akyildiz
Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Abstract
We consider the system of nonlinear differential equations governing shallow water waves over a uniform or sloping bottom. By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations. We show that these constructions are canonical relative to a symplectic form introduced by Manin.