경사면에서의 두 파의 상호작용에 관한 연구

Interaction of two surface waves over a slope is studied within the shallow water approximation. In is well known that the solutions of the linear shallow water equation over a slope can be expressed in the terms of Bessel functions. When trying to find the nonlinear correction in the form of quadratic expression of Bessel-type functions, the usual perturbation techniques inevitably leads to a series of over determined systems of linear algebraic equation for the unknown coefficients. The result is that all these over determined systems are compatible, which allow presenting explicitly a nonlinear solution as a quadratic polynomial of the Bessel-type functions. The solution describes two-waves interaction and is found with the same accuracy as the nonlinear shallow water equation is derived. Analogous formulas for cubic nonlinear corrections are also derived.