二维广义色散长波方程的显式行波解Traveling Wave Solutions of 2-Dimensional Generalized Dispersive Long Wave Equations
何宝钢,徐昌智
摘要(Abstract):
用辅助方程法构建二维广义色散长波方程的精确解 .经行波法约化方程 ,根据领头项分析 ,给出了这个模型的一个变换 ,利用非线性立方 Klein- Gordon方程的解 ,获得二维广义色散长波方程丰富的显式行波解 (包括孤波解 ,周期波解 ,雅可比椭圆函数解和其他精确平面波解 ) .
关键词(KeyWords): 辅助方程;广义色散长波方程;显式行波解
基金项目(Foundation): 浙江省自然科学基金资助项目 ,编号 10 0 0 3 9
作者(Author): 何宝钢,徐昌智
参考文献(References):
- [1] FanEngui,ZhangHongqing.A note on the hom ogeneous balance m ethod.PhysL ettA,1998,246:403~406.
- [2] ZhangJiefang,GuoGuanping,WuFengm in.New multi- soliton solutions and traveling wave solutions of the dispersivelong- wave equations.ChinPhys,2002,11(6):533~536.
- [3] 郑春龙,张解放.(2+1)维Camassa-Holm方程的相似约化与解析解.物理学报,2002,51(11):2426~2430.
- [4] ZhengChunlong,ZhangJiefang.General solution and fractal localized structures for the(2+1)- dimensional generalizedAKNS system.ChinPhysL ett,2002,19(10):1399~1402.
- [5] 徐昌智,张解放.(2+1)维非线性Burgers方程分离变量解和新型弧子结构.物理学报,2004,53(8):2407~2412.
- [6] XuChangzhi,ZhangJiefang.Variable separation solution for(1+1)- dimensional nonlinear m odels related toSchrodinger equation.Com munTheorPhys,2004,42:568~572.
- [7] WangMingliang,ZhouYubin,L iZhibin.Application of a hom ogeneous balance method to exact solutions of nonlinearequations in mathem atical physics.PhysL ett,1996,216:67~75.
- [8] ChenChunli,TangXiaoyan,L ouSenyue.Solutions in a(2+1)- dimensional dispersive long wave equation.PhysRevE66,036605.
- [9] 闫振亚,张鸿庆.(2+1)维非线性长波方程的相似约化和解析解.数学物理学报,2001,21A(3):384~390.
- [10] L iHuamei.The soliton solution of(3+1)- dim ensionalKadomtsev-Petviashvili equations.Comm unTheoyPhys,2002,37:561~563.
- [11] L iHuamei.Searching for the(3+1)- dim ensionalPainlevé integrable model and its solitary wave solution.ChinPhysL ett,2002,19:745~747.
- [12] FanEngui.Extended tanh- function method and its application to nonlinear equations.PhysL ett,2002,A277(4):212~218.
- [13] 刘式达,傅遵涛,刘式适.非线性波动方程的Jacobi椭圆函数包络周期解.物理学报,2002,51(4):718~722.