The shallow water equations: conservation laws and symplectic geometry - Yilmaz Akyildiz (International Journal of Mathematics and Mathematical Sciences)
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.