Study on the interaction of nonlinear water waves considering random seas

Abstract

The nonlinear Schrödinger equation plays an important role in wave theory, nonlinear optics and Bose-Einstein condensation. Depending on the background, different analytical solutions have been obtained. One of these solutions is the soliton solution. In the real ocean sea, interactions of different water waves can be observed at the surface. Therefore the question arises, how such nonlinear waves interact. Of particular interest is the interaction, also called collision, of solitons and solitary waves.

Using a spectral scheme for the numerical computation of solutions of the nonlinear Schrödinger equation, the nonlinear wave interaction for the case of soliton collision is studied. Thereby, the influence of an initial random wave is studied, which is generated using a Pierson-Moskowitz spectrum.