一类变分反问题的两种积变分方法及其应用

Two Integral-variation Methods and Applications to a Class of Inverse Variation Problem

针对 Kd V方程势函数的变分反问题所建立的一类积变分变分反问题的两种积变分方法 ,待定系数法和直接积变分法 ,推广应用到 m Kd V方程和 Harry Dym方程势函数的变分反问题 .两种有效计算方法的有关计算与判定都可以通过 MATHEMATICA计算机建立的软件来实现 .

In this paper, two integral variation methods, method of undetermined coefficients and method of direction variation integration, which were first set up for the inverse variation problem of potential functions on KdV equation, are respectively applied to the inverse variation problem of the mKdV equation and the Harry Dym equation. These calculations and decisions are accomplished by the MATHEMATICA software.