若干非线性PDEs守恒律的构造

Construction of Conservation Laws for Some Nonlinear Partial Differential Equations

利用对称-共轭对称‘对’方法和Ibragimov新守恒定理分别构造出Euler-Lagrange-type方程、CauchyKovalevskaya方程组及(2+1)维热方程中的诸多守恒律,同时通过对比已得守恒律发现两种守恒律方法的等价关系。结果对深入研究给定PDEs相关属性方面具有重要的理论意义。

Conservation laws are important in the solution and reduction of the partial differential equations(PDEs) and have become hot research topic recently. Several conservation laws of Euler-Lagrangetype equation, Cauchy-Kovalevskaya equations and(2+1)-dimensional heat equation are constructed by using symmetry/adjoint symmetry pair method and Ibragimov’s new conservation theorem respectively.Meanwhile, the equivalence relation of conservation laws constructed by the two methods is confirmed through comparing them. The results are of important theoretical significance for further studying the related properties of the given PDEs.