扩展的(2+1)维Jaulent-Miodek方程的显式解和守恒律  

Explicit Solutions,Conservation Laws of the Extended(2+1)-dimensional Jaulent-Miodek Equation

作　　者：李玉[1] 刘希强[1] 辛祥鹏[1] 

机构地区：[1]聊城大学数学科学学院

出　　处：《河北师范大学学报（自然科学版）》2016年第5期376-384,共9页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11505090);山东省优秀青年科学研究基金(BS2015SF009)

摘　　要：通过直接对称方法,得到了扩展的(2+1)维Jaulent-Miodek方程的经典李对称,并且利用对称得到了该方程的相似约化方程和群不变解.通过解约化方程得到了大量新的精确解,其中包括Weierstrass周期解、椭圆周期解、三角函数解等.最后,利用得到的对称和共轭方程,求得了该方程的守恒律.By applying the direct symmetry method, the classical Lie symmetry for the extended （2＋1）-dimensional Jaulent-Miodek equation were obtained, and further the symmetry reductions and group in- variant solutions were obtained from this symmetry. Many new exact solutions of this equation were obtained through the symmetry, which include Weierstrass periodic solutions, elliptic periodic solutions, and triangular function solutions. Finally, the conservation laws of the equation were obtained by using the symmetry and adjoint equations.

关 键 词：Jaulent-Miodek方程 李点对称 相似约化 精确解 守恒律 

分 类 号：O175.2[理学—数学]