NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (7): 788-793.

NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

夏铁成, 张鸿庆, 闫振亚

Department of Mathematics, Dalian University of Technology, Dalian 116024, P. R. China

收稿日期:2000-05-08 修回日期:2001-03-23 出版日期:2001-07-18 发布日期:2001-07-18
基金资助:
the National Key Basic Research Development Project of China(1998030600);the National Natural Science Foundation of China(10072013);the Doctoral Program Foundation of Institution of Higher Education of China(98014119)

NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

XIA Tie-cheng, ZHANG Hong-qing, YAN Zhen-ya

Department of Mathematics, Dalian University of Technology, Dalian 116024, P. R. China

Received:2000-05-08 Revised:2001-03-23 Online:2001-07-18 Published:2001-07-18
Supported by:
the National Key Basic Research Development Project of China(1998030600);the National Natural Science Foundation of China(10072013);the Doctoral Program Foundation of Institution of Higher Education of China(98014119)

摘要/Abstract

摘要： With the help of Mathematica, many travelling for a class of nonlinear evolution equations u_tt+au_xx+bu+cu²+du³=0 are obtained by using hyperbola function method and WU-elimation method, which include new travelling wave solutions, periodic solutions and kink soliton solutions. Some equations such as Duffing equation, sin-Gordon equation, 4 and Klein-Gordon equation are particular cases of the evolution equations. The method can also be applied to other nonlinear equations.

中图分类号:

O175.29

夏铁成;张鸿庆;闫振亚. NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(7): 788-793.

XIA Tie-cheng;ZHANG Hong-qing;YAN Zhen-ya . NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(7): 788-793.

[1]	Wancheng SHENG;Ying ZENG. Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 353-364.
[2]	张乔夫;崔俊芝. Existence theory for Rosseland equation and its homogenized equation[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1595-1612.
[3]	M.B.A.Mansour. Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(4): 513-516.
[4]	林苏榕;莫嘉琪;. 超抛物型方程的非线性奇摄动问题[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1377-1381 .
[5]	莫嘉琪;. 具有边界摄动弱非线性反应扩散方程的奇摄动[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(8): 1105-1110 .
[6]	A.卡努里;N.麦希迪. 具有 Cauchy-Ventcel边界条件的有界域中亚临界半线性波方程的稳定与控制[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(6): 787-800 .
[7]	杨柳;何斌吾. Applications of new affine invariant for polytopes[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(2): 273-278 .
[8]	房少梅;郭柏灵. Initial-boundary value problem of one class of nonlinear Schrödinger equations described in molecular crystals[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(2): 139-144 .
[9]	王艳萍;郭柏灵. Blow-up of solution for a generalized Boussinesq equation[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(11): 1437-1443 .
[10]	张丽;刘三阳. Bifurcation and pattern formation in a coupled higher autocatalator reaction diffusion system[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(9): 1235-1248 .
[11]	施惟慧;王曰朋. Impact of singularity of Navier-Stokes equation upon atmospheri motion equations[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(5): 689-693 .
[12]	甘在会;张健. Global solution for coupled nonlinear Klein-Gordon system[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(5): 677-687 .
[13]	施惟慧;王曰朋. Stability of theoretical model for catastrophic weather prediction[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(4): 553-561 .
[14]	施惟慧;徐明;王曰朋. Stability for basic system of equations of atmospheric motion[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(2): 261-268 .
[15]	何卷雄;何幼桦. CAUCHY PROBLEM OF ONE TYPE OF ATMOSPHERE EVOLUTION EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(10): 1409-1416 .

NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价