(2+1)维Kadomtsev-Petviashvili方程的留数对称及其相互作用解  

Residual Symmetry and Interaction Solution of the(2+1)-Dimensional Kadomtsev-Petviashvili Equation

作　　者：葛楠楠 任晓静 GE Nannan;REN Xiaojing(School of Mathematics, Northwest University, Xi'an 710127, China)

机构地区：[1]西北大学数学学院

出　　处：《应用数学》2019年第4期778-784,共7页Mathematica Applicata

基　　金：国家自然科学基金(11775047)

摘　　要：运用Painleve截断展开方法得到(2+1)维Kadomtsev-Petviashvili(KP)方程的非局域留数对称和Backlund 变换.由于非局域对称不能直接对(2+1)维KP方程进行约化求解,因此,需要将非局域对称局域化.然后,利用相容的Riccati展开(CRE)可解的概念证明(2+1)维KP方程的CRE可解性,从而求出(2+1)维KP方程的新的相互作用解.The truncated Painlev e expansion method is developed to obtain the nonlocal residual symmetry and Backlund transformation for the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation. The nonlocal symmetry cannot directly solve the (2+1)-dimensional KP equation. It is necessary to localized the nonlocal symmetry . Then, using the solvable concept of the consistent Riccati expansion method (CRE), the (2+1)-dimensional KP equation is proved to be consistent Riccati expansion solvable, and the new interaction solution of the (2+1)-dimensional KP equation is obtained.

关 键 词：(2+1)维KP方程 留数对称 Painleve截断展开 CRE可解 相互作用解 

分 类 号：O175.14[理学—数学]