CAJ | 학술논문

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-GibbonSawada-Kotera方程、Boiti-Leon-Manna-Pempinelli方程和(2+1)-维Burgers方程以及It(o)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).
제출료구조비선성편미분방정고계수항률적직접법병재Maple상실현,산법역조작,효솔고.작위산법적응용,고필료허다고유비선성편미분방정,여Caudrey-Dodd-GibbonSawada-Kotera방정、Boiti-Leon-Manna-Pempinelli방정화(2+1)-유Burgers방정이급It(o)방정조,득도료타문적신적고계수항률.해산법환가용우구조경고유경고계적수항률,역가추엄지미분-차분방정(조).
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.