Abstract
The soliton evolution on the water surface in the case of an inclined bottom is considered within the shallow water approximation. The Riemann function method is used to obtain the linear solution. It is shown that the 2nd-, 3rd-, and 4th-order nonlinear corrections are expressed in terms of the derivatives of the function defining the linear solution. The solution obtained can be applied to the description of the tsunami wave propagation in the coastal area.
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