(2+1)维KD方程的扰动非行波双孤子和周期解

The Perturbed Non-traveling Wave Double Solitary and Periodic Solutions for (2+1)-D KD Equation

摘要:

应用退耦变换和Lie对称群方法，将(2+1)维KD方程的约化成了(1+1)维非线性PDE。通过广义同宿测试法获得了该方程新的扰动非行波双孤子解及其动力学临界点和参数极限情况下的非行波有理函数奇解。运用二维平面动力系统的Hamilton函数讨论了对称约化方程在波变换下的周期解存在性，并用正切函数拟设法得到了该周期解的显式精确表达，相应获得了KD方程的扰动非行波周期解析解。

Abstract:

Based on the decoupling transformation and the Lie point symmetry group method, the (2+1)-D KD equation is reduced to the (1+1)-D nonlinear PDE. By extended homoclinic test approach, new perturbed non-traveling wave double solitary solutions of the (2+1)-D KD equation are obtained. Also, the dynamic critical point and the non-traveling wave rational function singular solutions in the limitation of parameters are derived. Applying the Hamilton function in 2-D planar dynamical system, we discuss the existence of the periodic solutions for the symmetrical and reduced equation with the wave transformation. Moreover, some periodic solutions are derived by the Tan-function test method, and the perturbed non-traveling wave periodic solutions for the (2+1)-D KD equation are shown.