T.S. Jang

Nonlinear wave interaction of three Stokes’ waves in deep water: Banach fixed point method

Based on Banach fixed point theorem, a method to calculate nonlinear superposition for three interacting Stokes’ waves is proposed in this paper. A mathematical formulation for the nonlinear superposition in deep water and some numerical solutions were investigated. The authors carried out the numerical study with three progressive linear potentials of different wave numbers and succeeded in solving the nonlinear wave profiles of their three wave-interaction, that is, using only linear wave potentials, it was possible to realize the corresponding nonlinear interacting wave profiles through iteration of the method. The stability of the method for the three interacting Stokes’ waves was analyzed. The calculation results, together with Fourier transform, revealed that the iteration made it possible to predict higher-order nonlinear frequencies for three Stokes’ waves’ interaction. The proposed method has a very fast convergence rate.