2_1_维扩散长水波方程的衰变解和其它精确解.pdf

29 1 Vol. 29 No. 1 2003 3 Journal of Gansu University of Tec nology Mar. 2003 :2003) 2+ 1维扩散长水波方程的衰变解和其它精确解 1, 2 1 夏铁成 , 张鸿庆 ( 1. , 116024; 2. , 121000) : 应用齐次平衡法获得了2+ 1 维扩散长水波方程的Bcklund 变换和一 个线 偏微分方程. 从线 偏微分方程 出发得到了2+ 1维扩散长水波方程的多孤子解和单孤子解以及其它精确解, 分析单孤子解, 获得了衰变结构. : (2+ 1)维扩散长方波方程; Bcklund 变换; 齐次平衡法; 孤子解; 精确解; 衰变解 : O175. 29 : A Dromion and other exact solutions of ( 2+ 1)dimensional dispersive long wave equation XIA Tiec eng1,2 , ZHANG Hongqing1 ( 1. Dept. of Applied Mat ematics, Dalian University of Tec nology, Dalian 116024, C ina; 2. Dept. of Mat ematics, Jinz ou Normal College, Jinz ou 121000, C ina) Abstract: Using omogenous balance met od an autoBcklund transformation of ( 2+ 1)dimensional dispersive long wave equation and a derived linear partial differential equation are obtained. As a result, t e multisoliton and single soli ton and ot er exact solutions of ( 2+ 1)dimensional dispersive long wave equation are derived from abovementioned dif ferential equation. By analyzing single soliton solution, some dromion solutions are obtained. Key words: ( 2+ 1)dimensional dispersive long wave equation; autoBcklund trans transformation; omogenous bal ance met od; soliton solutions; exact solution; dromion solution [ 1] [4] 1834 KP , . [2] [ 6,7] KdV Gardner , ( 2+ 1) . 1967 , ( 2 + 1) Kac MoodyVirasoro( KMV) ,