一个可积非线性演化方程的达布变换及其精确解

Darboux Transformation and Exact Solutions for an Integrable Nonlinear Evolution Equation

研究了一个新的可积非线性演化方程,基于其Lax对和谱问题的规范变换,构造出该方程的一个达布变换,进而利用此达布变换,得到该方程的精确解,包括有理解、孤子解与周期解.

A new integrable nonlinear evolution equation was proposed. Based on the resulting Lax pair,a Darboux transformation of the nonlinear evolution equation was structured with the aid of the gauge transformation, by which some exact solutions of the nonlinear evolution equation were obtained, inclu- ding rational solutions, soliton solutions and periodic solutions.