Direct algorithms for constructing high-order conservation laws of nonlinear partial differential equations〖CB〗

提出了构造非线性偏微分方程高阶守恒律的直接法并在Maple上实现,算法易操作,效率高.作为算法的应用,考虑了许多高维非线性偏微分方程,如Caudrey-Dodd-Gibbon-Sawada-Kotera方程、Boiti-Leon-Manna-Pempinelli方程和(2+1)-维Burgers方程以及It?方程组,得到了它们的新的高阶守恒律.该算法还可用于构造更高维更高阶的守恒律,亦可推广至微分-差分方程(组).

Direct algorithms for constructing high-order conservation laws of nonlinear partial differential equations

The direct algorithms for constructing the conservation laws of nonlinear differential equations are put forward and implemented in software Maple,which are easy for operation and high efficiency. As applications of the algorithms,some higher-dimensional nonlinear differential equations,such as Caudrey-Dodd-Gibbon-Sawada-Kotera equation,Boiti-Leon-Manna-Pempinelli equation and(2+1)-dimensional Burgers equation together with It(o) equations are considered .As a result,some new high-order conservation laws of these equations have been obtained. The algorithms can be used to construct more higher order and dimension of conservation laws and be generalized to differential-difference equations.