摘要
孤子方程是非线性科学领域中的一个重大研究课题,它是一门涉及多学科、多领域的研究领域,研究手段和方法很多,但是达布变换是一种经典而美妙的方法。本文根据KN方程的Lax对,借助KN方程的谱问题和规范变换,最终构造出一个含有多个参数的达布变换.通过此变换,求得KN方程的孤子解,并且讨论了n=1和n=2两种孤子解的特殊情况。
Soliton equations is an important research subject in the field of nonlinear science, it is a multi-disciplinary, multi field research field, many research means and methods, but the Darboux transformation is a method of classic and beautiful. In this paper, according to the KN equation by means of the Lax spectral problem and the canonical transformation, KN equation finally, construct a parameterization of the Darboux transformation. By this transformation, the soliton solutions of the KN equation are obtained, and discussed the special cases and two soliton solution.
出处
《科技通报》
北大核心
2016年第6期17-20,23,共5页
Bulletin of Science and Technology
基金
河南省现代产业体系动力机制研究(项目编号:142400410264)
关键词
KN方程
达布变换
孤子解
KN equation
Darboux transformation
soliton solutions
