Boussinesq方程的非古典对称和相容性  

Nonclassical symmetries of the Boussinesq equation and compatibility

作　　者：蔡国梁[1] 王燕[1] 张风云[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2007年第5期457-460,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(90210004);江苏省教育厅基金资助项目(03SJB790008);江苏大学高级人才基金资助项目(07JDG054)

摘　　要：研究了一类任意阶的非线性偏微分方程的非古典对称的决定方程,比较了非古典对称和古典对称求解方法的不同,在求解非线性古典对称的过程中,引用了一个简单的偏微分方程,运用向量场和其延拓以及不变表面条件和初始方程的相容性两种方法求出了相同的非古典对称的决定方程,由此,得出了利用不变表面条件和初始方程的相容性也可以求得非线性偏微分方程的非古典对称的重要结论.以Boussinesq方程为例,证明了该结论的可行性.The determining equations for the nonclassical symmetries of a class of nonlinear classical partial differential equations with arbitrary orders are studied. The result is compared with the classical sym- metry. A simple partial differential equation is quoted to get the conclusion that the nonclassical symmetry of the nonlinear partial differential equations can be derived through the compatibility between the original equation and the invariant surface condition. Finally, the Boussinesq equation is discussed to prove the conclusion

关 键 词：BOUSSINESQ方程 非古典对称 决定方程 不变表面条件 相容性 

分 类 号：O175[理学—数学]