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Application of variable coefficient KdV equation to solitary waves in the ocean. (Chinese. English summary) Zbl 1463.35435

Summary: This paper mainly discusses a solution method and its theoretical application of the variable coefficient KdV equation. Firstly, the initial value condition is given by the analytical solution, and then the equation is discretized by the Runge-Kutta method combined with the explicit format difference method, and the MATLAB software is used to calculate the numerical solution of the equation. In order to reflect the characteristics of solitary waves better, this paper selects different initial waveforms, studies the typical cases of polar wave transformation, linearization and dispersion to generate wake waves, and applies this theory to the solitary wave of actual oceans in order to understand the characteristics of the inner solitary wave more concisely and intuitively.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
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