Abstract

Surface waves motion over a slope is studied within the shallow water approximation and solutions of the equation are expanded in series in wave amplitude. It is shown that if a linear solution is known, the nonlinear corrections can be obtained in the terms of it’s derivatives. If the amplitude is sufficiently small, the constructed sequence converges to an exact solution of the shallow water equation for a wide class of problems. The quadratic problem is considered and it is shown that the nonlinear wave is of the bigger amplitude and steepness than the linear one.

中文翻译：

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斜坡上的表面波

摘要

在浅水近似中研究了在斜坡上的表面波运动，并且方程的解在波振幅上被串联扩展。结果表明，如果已知线性解，则可以根据其导数获得非线性校正。如果幅度足够小，则针对一系列问题，构造的序列将收敛到浅水方程的精确解。考虑了二次问题，结果表明非线性波的振幅和陡度比线性波的振幅和陡度大。