PHENOMENA ON ROGUE WAVES AND RATIONAL SOLUTION OF KORTEWEG-DE VRIES EQUATION

摘要

An appropriate nonlinear mechanism may create the rogue waves. Perhaps the simplest mechanism, which is able to create considerate changes in the wave amplitude, is the nonlinear interaction of shallow-water solitons. The most well-known examples of such structure are Korteweg-de Vries (KdV) solitons. The Korteweg-de Vries (KdV) equation, which describes the shallow water waves, is a basic weakly dispersive and weakly nonlinear model. Basing on the homogeneous balanced method, we achieve the general rational solution of a classical KdV equation. Numerical simulations of the solution allow us to explain rare and unexpected appearance of the rogue waves. We compare the rogue waves with the ones generated by the nonlinear Schrodinger (NLS) equation which can describe deep water wave trains. The numerical results illustrate that the amplitude of the KdV equation is higher than the one of the NLS equation, which may causes more serious damage of engineering structures in the ocean. This nonlinear mechanism will provide a theoretical guidance in the ocean and physics.