广义Hirota-Satsuma耦合KdV方程的对称及应用  

The admitted symmetries of the generalized Hirota-Satsuma coupled KdV equation and applications

作　　者：康周正[1] 任文秀[1] 王善微[1] 

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《黑龙江大学自然科学学报》2011年第6期813-817,共5页Journal of Natural Science of Heilongjiang University

基　　金：内蒙古自治区自然科学基金资助项目(20080404MS0106);内蒙古工业大学校重点基金资助项目(ZD200813)

摘　　要：将广义Hirota-Satsuma耦合KdV方程作为研究对象,首先借助古典Lie点对称法研究了它的对称群理论,并且利用对称群的思想得到了四组新形式的精确解;其次,探讨了该方程允许的全部四阶对称;最后,作为对称在物理上的重要应用,还进一步地分情形给出了它的五条守恒律。The generalized Hirota -Satsuma coupled KdV equation is taken as the research object, the symmetry group theorem is firstly considered by means of the classical Lie point symmetry method. Then, the new explicit and exact solutions under the groups are obtained. Secondly, all the admitted four -order symmetries are studied. Finally, the equation＇ s five conservation laws in cases are also given, which are regarded as the symmetry＇ s important application in physics.

关 键 词：Lie对称群 精确解 四阶对称 守恒律 

分 类 号：O175[理学—数学]