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Generalized Nonlinear Equation and Solutions for Fluid Contour Deformations

A. Ludu·A. R. Ionescu
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Abstract

We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a finite-difference expression, with a general solution that is a power series expansion with coefficients satisfying a nonlinear recursion relation. In the limit of long and shallow water, we recover the Korteweg-de Vries equation together with its single-soliton solution.

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A. Ludu, A. R. Ionescu. 2002-01-25. Generalized Nonlinear Equation and Solutions for Fluid Contour Deformations. https://arxiv.org/abs/math-ph/0201056

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