两个generalized Hirota-Satsuma coupled KdV方程的守恒律

Conservation laws of two generalized Hirota-Satsuma coupled KdV equations

目的研究两个generalized Hirota-Satsuma coupled KdV(GH-S CKdV)方程拥有的守恒律问题。方法根据齐次微分方程的等秩性质,利用Euler-Lagrange方程变分原理及同伦算子构造非线性PDE的多项式形式的守恒律。结果与结论得到了两个GH-S CKdV方程部分不显示依赖于自变量的多项式守恒律,其结果对研究方程的可积性和分析其解的性质具有重要作用。

Aim To study the conservation laws of two generalized Hirota-Satsuma coupled KdV equations（GH-S CKdV）.Methods Polynomial conservation laws of nonlinear PDE are constructed using the variational principles of Euler-Lagrange equation and homotopy operators based on the rank properties of homogeneous differential equation.Results and Conclusions In the term of this methods,poylnomial conservation was of two GH-S CKdV equations which depend only on the dependent variables and their derivatives but not on the independent variables is obtained,this result plays an important role in studying the integrability and analyzing the properties of the solutions.