摘 要:由于非线性引起的脉冲的挤压与由色散引起的扩展相互抵消,可以使行波保持一个永久的形状,从而导致非线性色散方程孤子解的产生,据此我们修改KdV方程的非线性项,并利用齐次平衡原则获得了这类广义KdV方程的孤子解。
关键词:KdV方程 齐次平衡原则 孤立子
中图分类号:O175.14 文献标识码:A 文章编号:1672-3791(2011)01(b)-0162-02
Abstract:For nonlinear dispersion equation,because of mutual offset of nonlinear impulsive caused by effect of nonlinearity and expanding caused by the effect of dispersion,a permanent wave shape can be maintained to form of the solution of soliton.Based on this fact,we modify the nonlinear term of KdV equation and use the homogeneous balance principle to obtain the soliton solution of this socalled generalized KdV equation.
Key words:KdV Equation;Homogenous balance principle;Soliton
孤子是上世纪非线性科学的重要发现,有关孤子的最早描述可见于1834年Scott Russell对河面上单个凸起的水峰的保形运动。其后,在1895年荷兰数学家Korteweg和de Vries导出了著名的KdV方程: