New Periodic Wave Solutions and Their Interaction for （2＋1）-dimensional KdV Equation  

作　　者：GE Dong-jie MA Hong-cai YU Yao-dong 

机构地区：[1]College of Science, Donghua University, Shanghai 201620, China

出　　处：《Chinese Quarterly Journal of Mathematics》2009年第4期525-536,共12页数学季刊（英文版）

基　　金：Foundation item： Supported by the National Natural Science Foundation of China（10647112, 10871040） Acknowledgement The authors are in debt to thank the helpful discussions with Prof Qin and Dr A P Deng.

摘　　要：A class of new doubly periodic wave solutions for （2＋1）-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution（contains two arbitrary functions） got by means of multilinear variable separation approach for （2＋1）-dimensional KdV equation. Limiting cases are considered and some localized excitations are derived, such as dromion, multidromions, dromion-antidromion, multidromions-antidromions, and so on. Some solutions of the dromion-antidromion and multidromions-antidromions are periodic in one direction but localized in the other direction. The interaction properties of these solutions, which are numerically studied, reveal that some of them are nonelastic and some are completely elastic. Furthermore, these results are visualized.

关 键 词：（2＋1）-dimensional KdV equation multilinear variable separation approach elliptic functions periodic wave solutions localized excitations interaction property nonelastic completely elastic 

分 类 号：O175.29[理学—数学] O411.1[理学—基础数学]