Solitary wave and similarity solutions of the combined KdV equation

In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that the combined KdV equation can be reduced to the Painlevé equation. Furthermore, utilizing special transformations of similarity variables, we derive a kind of new partial differential equations.     

SOLITARY WAVE AND SIMILARITY SOLUTIONS OF THE COMBINED KdV EQUATION

In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that the combined KdV equation can be reduced to the Painleve equation. Furthermore, utilizing special transformations of similarity variables, we derive a kind of new partial dtfferential equations.     

关于带非均匀项KdV方程的求解

本文研究带非均匀项的KdV方程(1)的反散射解。得到了当Schr(?)din ger方程的位势u按方程(1)演化时,它的散射量随时间t的演化规律。并利用反散射方法求出了方程(1)的孤子解。     

组合KdV方程的孤立波解与相似解

本文讨论组合KdV方程孤立波解的一个性质,指出该方程可化为Painlevé方程,并利用相似变量的特殊变换导出一类新的偏微分方程.     

带非均匀项Kdv方程的Bcklund变换

本文利用Miura变换说明带非均匀项KdV方程可化为反散射形式,从此导出该方程的B(?)cklund变换。