A new approach to analyze nonlinear standing waves

Abstract An accurate and simple analysis for nonlinear gravity standing waves is suggested in this paper. The nonlinearity of wave profile is introduced to maintain the implicit function, and the interaction terms are worked out by using the Lagrange's expansion method. For the convenience of applications, the relationships between the standing waves and their corresponding source of incident progressing waves are formulated in this study. The results are in good agreement with both the higher order solution and the experimental data performed by predecessors.