一个(3+1)维非线性偏微分方程的有限对称变换群和精确解  

Finite Symmetry Transformation Groups and Some Exact Solutions of a (3+1)-dimensional Nonlinear Evolution Equation

作　　者：王美丽[1] 李彪[1] 

机构地区：[1]宁波大学理学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2015年第4期96-99,共4页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(11271211)

摘　　要：基于符号计算与对称群直接法研究了一个(3+1)维非线性偏微分方程3wxz-(2wt-2wwx+wxxx)y+2(wxx-1wy)x=0的对称群与精确解,获得该方程的李点对称群和非李对称群.最后通过广义射影Riccati展开法研究方程的精确解,并由获得的有限对称变换群构造了相应新的一般解.Based on symbolic computation and the symmetry group direct method, we investigate symmetry groups and exact solution of a （3＋l）-dimensional nonlinear evolution equation 3wz-（2wt -2wwx ＋ Wxxx）y ＋ 2（wxЭ^-1xwy）x = 0, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. Finally, using a generalized sub-equation expansion method, some exact solutions of the （3＋1）-dimensional nonlinear evolution equation are derived, and the corresponding new solutions can be constructed through the finite symmetry transformation groups obtained.

关 键 词：对称群 精确解 符号计算 (3+1)维NEE方程 广义射影Riccati展开法 

分 类 号：O175.29[理学—数学]