Generalized Nonlinear Equation and Solutions for Fluid Contour Deformations
数学物理
2007-05-23 v1 动力系统
math.MP
摘要
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.
引用
@article{arxiv.math-ph/0201056,
title = {Generalized Nonlinear Equation and Solutions for Fluid Contour Deformations},
author = {A. Ludu and A. R. Ionescu},
journal= {arXiv preprint arXiv:math-ph/0201056},
year = {2007}
}