DEFORMATION OF NONLINEAR SHALLOW WATER WAVES.

Deformation of nonlinear shallow water waves including small dispersive effect is studied. Specifically, deformation of an initial wave of solitary-type in water of uniform depth is studied using conservation laws and eigenvalue method. The dependence of number and heights of generated solitons upon nondimensional parameter beta which is inversely proportional to the Ursell parameter of the initial wave, is established. It is shown that the results based on the conservation laws agree fairly well with those by the eigenvalue method for the case of large beta . Time and space scales related to the deformation of a wave in water of uniform depth are estimated. A law of the frictional damping is also derived by using the conservation laws of this equation.