广义Hirota-Satsuma耦合KdV方程的对称及应用

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.