Some Exact Solutions of the NLS Equation for Deep-water Waves

摘要

Whitham derived the nonlinear Schr?dinger equation from the mostrngeneral form of the nonlinear wave dispersion relation. The NLSrnequation was analyzed from the second-order Stokes’ nonlinear deepwaterrnwave dispersion relation. The exact solutions of the nonlinearrnwave were obtained by using modified mapping method. As thisrnspecialization of this equation, the solutions were different from thatrnhad been obtained and contained the Debnath’s solutions. From thernform and the character of the solutions, the relation of the solutions wasrnanalyzed and these can be classified to three kinds.