变系数KdV方程和变系数MKdV方程的无穷多守恒律

CONSERVATION LAWS OF THE VARIABLE COEFFICIENT KdV AND MKdV EQUATIONS

本文利用Miura方法研究具有三个任意函数的变系数KdV方程和变系数MKdV方程的无穷多守恒律,结果表明:守恒密度仅与一个任意函数有关,并且与常系数KdV(和MKdV)方程的守恒密度有完全类似的结构,另两个任意函数仅包含于相应的流密度中。

In this paper, by using the Miura's method, we study the infinite conservation laws of the variable coefficient KdV and MKdV equations with three arbitrary functions of t. The result points out that the conserved densities which have the structures completely similar to the con-stat coefficient KdV and MKdV equations depend only on one arbitrary function. The other two arbitrary functions are contained only in the corresponding fluxes.