摘要
本文中我们考虑了五阶KdV方程,变形KdV方程和Ito方程以及相关的一些问题。我们给出了五阶KdV方程和二次变形的五阶KdV方程的Backlund变换(简称BT)及非线性叠加公式。利用Hirota的直接方法,我们求得了变形的五阶KdV方程的N-孤立子解。对于Ito方程,我们给出了其多参数的BT并导出了该方程的无穷多个守恒律。我们还考虑了五阶KdV方程及变形方程和Ito方程的BT与Scale变换之间的关系。此外,我们得到了五阶KdV方程的一个周期波解。
In this paper, a fifth order KdV equation and its modified equations and Ito equation as well as related problems are considered. We present Backlund transformations and nonlinear superposition formulae for the fifth order KdV equation and a second modified KdV equation. Using Hirota＇s direct method, we obtain N-soliton solutions to the modified fifth order KdV equation. We also get BT possessing three-parameter and infinitely many conservation laws concerning Ito equation. In addition, we establish the relations between Scale transformations and BTs for the fifth order KdV equation, the second modified KdV equation and Ito equation. We also obtain one-periodic wave solution to fifth order KdV equation.
出处
《同济大学学报（自然科学版）》
EI
CAS
CSCD
1989年第3期377-384,共8页
Journal of Tongji University:Natural Science
