STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (8): 925-934.

STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS

闫振亚, 张鸿庆

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

收稿日期:2000-04-07 修回日期:2001-03-13 出版日期:2001-08-18 发布日期:2001-08-18
基金资助:
the National Key Basic Research Project Foundation of China(G1998030600);Doctoral Foundation of Education Committee(98014119)

STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS

YAN Zhen-ya, ZHANG Hong-qing

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

Received:2000-04-07 Revised:2001-03-13 Online:2001-08-18 Published:2001-08-18
Supported by:
the National Key Basic Research Project Foundation of China(G1998030600);Doctoral Foundation of Education Committee(98014119)

摘要/Abstract

摘要： The homogeneous balance method was improved and applied to two systems of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang’s and Zhang’s results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.

中图分类号:

O175.1

闫振亚;张鸿庆. STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(8): 925-934.

YAN Zhen-ya;ZHANG Hong-qing. STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(8): 925-934.

参考文献

[1] Ablowitz M J, Clarkson P A. Solitons, Nonlinear Evolution Equations and Inverse Scattering [M]. Cambridge: Cambridge University Press,1991.
[2] Gu C H, Li Y S. Tian C, et al. Solitons Theory and Its Applications [M]. Berlin: SpringerVerlag, 1995.
[3] GUO Bo-ling, PANG Xiao-feng. Solitons[M]. Beijing: Science Press, 1987. (in Chinese
[4] Wang M L, Zhou Y B, Li Z B. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics[J]. Phys Lett A, 1996,216(1):67-75.
[5] Whitham G M. Variational methods and applications to water wave[J]. Proc Roy Soc London Ser A ,1967,299(1):6-25.
[6] Broer L J. Approximate equations for long water waves[J]. Appl Sci Res, 1975,31(5):377-395.
[7] Kupershmidt B A. Mathematics of dispersive water waves [J]. Comm Math Phys, 1985,99 (1):51-73.
[8] Ruan H Y, Lou S Y. Similarity analysis and Painleve property of the Kupershmidt equation[J].Comm Theoret Phys ,1993,20(1):73-80.
[9] YAN Zhen-ya, ZHANG Hong-qing. Explicit and exact solutions for nonlinear approximate equations with long wave in shallow water [J]. Acta Phys Sinica, 1999,48(11):1962-1967.(in Chinese)
[10] ZHANG Jie-fang. Multiple soliton solutions for the approximate equations of long water wave [J].Acta Phys Sinica, 1998,47(9): 1416-1421. (in Chinese)
[11] ZHANG Jie-fang. Multiple solitons-like solutions for (2 + 1)-dimensional dispersive long wave equations[J]. Intern J Theoret Phys, 1998,37(9):2449-2455.
[12] Sach R L. On the integrable variant of the Boussinesq system, Painleve property, rational solutions, a related many body system, and equivalence with the AKNS hierarchy[J]. Physica D,1988,30(1): 1-27.
[13] FAN En-gui, ZHANG Hong-qing. Backlund transformation and exact solutions for WBK equations in shallow water [J] . Applied Mathematics and Mechanics (English Edition), 1998,19 (8):713 -716.

[1]	王海仁谢捷敏谢旋胡元太王骥. Nonlinear characteristics of circular-cylinder piezoelectric power harvester near resonance based on flow-induced flexural vibration mode[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(2): 229-236.
[2]	王方磊;安玉坤. 非线性电报方程组的3个双周期正解问题[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 81-88 .
[3]	雒志学;杜明银. 一类具年龄结构n维事物链模型的最优收获控制[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(5): 683-695 .
[4]	鲁铁军;王美娟;刘妍. Global stability analysis of a ratio-dependent predator-prey system[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(4): 495-500 .
[5]	李挺. Random attractors for asymptotically upper semicompact multivalue random semiflows[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(11): 1527-1534 .
[6]	张天四;朱德明. Bifurcations of double homoclinic flip orbits with resonant eigenvalues[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(11): 1517-1526 .
[7]	龙瑶;李继彬;芮伟国;何斌. Travelling wave solutions for a second order wave equation of KdV type[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(11): 1455-1465 .
[8]	陈丽华;莫嘉琪. Singularly perturbed solution for weakly nonlinear equations with two parameters[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(10): 1343-1348 .
[9]	冯大河;李继彬. Bifurcations of travelling wave solutions for Jaulent-Miodek equations[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 999-1005 .
[10]	李继彬;黎明;纳静. Kink wave determined by parabola solution of a nonlinear ordinary differential equation[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(7): 883-892 .
[11]	. Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(6): 799-809 .
[12]	尹福其;周盛凡;殷苌茗;肖翠辉. Global attractor for Klein-Gordon-Schrödinger lattice system[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(5): 695-706 .
[13]	肖海滨. Global analysis of Ivlev's type predator-prey dynamic systems[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(4): 461-470 .
[14]	张韧;洪梅;孙照渤;牛生杰;朱伟军;闵锦忠;万齐林. NON-LINEAR DYNAMIC MODEL RETRIEVAL OF SUBTROPICAL HIGH BASED ON EMPIRICAL ORTHOGONAL FUNCTION AND GENETIC ALGORITHM[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(12): 1645-1653 .
[15]	龙瑶;芮伟国;何斌;陈灿. BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR GENERALIZED DRINFELD-SOKOLOV EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(11): 1549-1555 .

STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS

STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS 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