ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS

doi:10.1016/S0252-9602(15)30052-7

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1241-1250.doi: 10.1016/S0252-9602(15)30052-7

• 论文 • 上一篇

ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS

袁文俊^1,2, Weiling XIONG³, Jianming LIN⁴, Yonghong WU⁵

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
2. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China;
3. Department of Information and Computing Science, Guangxi University of Technology, Liuzhou 545006, China;
4. School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou 510006, China;
5. Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth WA 6845, Australia

收稿日期:2012-12-02 修回日期:2015-03-02 出版日期:2015-09-01 发布日期:2015-09-01
通讯作者: Jianming LIN E-mail:ljmguanli@21cn.com
作者简介:Wenjun YUAN, E-mail: gzywj@tom.com; Weiling XIONG, E-mail: xiongwl@163.com; Jianming LIN, E-mail: ljmguanli@21cn.com; Yonghong WU, E-mail: y.wu@curtin.edu.au
基金资助:
The first author is supported by the NSFC (11271090) and NSF of Guangdong (S2012010010121).

ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS

Wenjun YUAN^1,2, Weiling XIONG³, Jianming LIN⁴, Yonghong WU⁵

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
2. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China;
3. Department of Information and Computing Science, Guangxi University of Technology, Liuzhou 545006, China;
4. School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou 510006, China;
5. Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth WA 6845, Australia

Received:2012-12-02 Revised:2015-03-02 Online:2015-09-01 Published:2015-09-01
Contact: Jianming LIN E-mail:ljmguanli@21cn.com
Supported by:
The first author is supported by the NSFC (11271090) and NSF of Guangdong (S2012010010121).

摘要/Abstract

摘要：

In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modified KdV equation, nonlinear Klein-Gordon equation and modified BBM equation. Our work shows that there exist some classes of rational solutions w_r,2(z) and simple periodic solutions w_s,1(z) which are new and are not degenerated successively to by the elliptic function solutions.

关键词: differential equation, exact solution, meromorphic function, elliptic function

Abstract:

Key words: differential equation, exact solution, meromorphic function, elliptic function

中图分类号:

30D35

袁文俊, Weiling XIONG, Jianming LIN, Yonghong WU. ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS[J]. 数学物理学报(英文版), 2015, 35(5): 1241-1250.

Wenjun YUAN, Weiling XIONG, Jianming LIN, Yonghong WU. ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS[J]. Acta mathematica scientia,Series B, 2015, 35(5): 1241-1250.

参考文献

[1] Conte R, Musette M. Elliptic general analytic solutions. Stud Appl Math, 2009, 123(1):63-81
[2] Eremenko A. Meromorphic solutions of equations of briot-bouquet type. Teor Funktsii, Funk Anal i Prilozh, 1982, 38:48-56; English Translation:Amer Math Soc Transl 1986, 133(2):15-23
[3] Eremenko A, Liao LW, Ng TW. Meromorphic solutions of higher order briot-bouquet differential equations. Math Proc Cambridge Philos Soc, 2009, 146(1):197-206
[4] Han Z X. New exact solutions for nonlinear Klein-Gordon equations. Acta Phys Sin, 2005, 54(4):1481-1484(in Chinese)
[5] Hassan H H. New exact solutions of two nonlinear physical models. Commun Theor Phys, 2010, 53:596-604
[6] Kudryashov N A. Meromorphic solutions of nonlinear ordinary differential equations. Commun Nonlinear Sci Numer Simul, 2010, 15(10):2778-2790
[7] Lang S. Elliptic Functions. 2nd ed. New York:Springer-Verlag, 1987
[8] Lü D Z. Abundant Jaccobi elliptic function solutions of nonlinear evolution equations. Acta Phys Sin, 2005, 54:4501-4505(in Chinese)
[9] Li B, Chen Y, Zhang H. Exact traveling wave solutions for a generalized Zakharov-Kuznetsov equation. Appl Math Comput, 2003, 146:653-66
[10] Li D S, Zhang H Q. A simple method for constructing elliptic function solutions to the nonlinear evolution equations and its applications. Acta Phys Sin, 2006, 55:1565-1570(in Chinese)
[11] Mei J Q, Zhang H Q. New soliton-like and periodic-like solutions for the KdV equation. Appl Math Comput, 2005, 169:589-599
[12] Peng Y Z. Exact traveling wave solutions for the Zakharov-Kuznetsov equation. Appl Math Comput, 2008, 199:397-405
[13] Wazwaz A M. The extended tanh method for the Zakharov-Kuznetsov ZK equation, the modified ZK equation, and its generalized forms. Commun Nonlinear Sci Numer Simulat, 2008, 13:1039-1047
[14] Wu H Y, Zhang L, Tan Y K, Zhou X T. Some new exact Jacobian elliptic function solutions of three kinds of nonlinear evolution equations. Acta Phys Sin, 2008, 57:3312-3318(in Chinese)
[15] Yomba E. Jacobi elliptic function solutions of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and t-dependent coefficients. Phy Lett A, 2010, 374:1611-1615
[16] Yuan W J, Shang Y D, Huang Y, Wang H. The representation of meromorphic solutions of certain ordinary differential equations and its applications. Scientia Sinica Mathematica, 2013, 43(6):563-575
[17] Zakharov V E, Kuznetsov E A. On three-dimensional solitons. Sov Phys JETP, 1974, 39:285-288
[18] Zhao X, Zhou H, Tang Y, Jia H. Traveling wave solutions for modified Zakharov-Kuznetsov equation. Appl Mathem Comput, 2006, 181:634-648

ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS

ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Bochra NEFZI, Kamel BRAHIM, Ahmed FITOUHI. ON THE FINITE MELLIN TRANSFORM IN QUANTUM CALCULUS AND APPLICATION[J]. 数学物理学报(英文版), 2018, 38(4): 1393-1410.
[2]	张建军, 廖良文. A NOTE ON MALMQUIST-YOSIDA TYPE THEOREM OF HIGHER ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2018, 38(2): 471-478.
[3]	韩月才, 孙一芳. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS[J]. 数学物理学报(英文版), 2018, 38(2): 681-694.
[4]	王志明. EULER SCHEME AND MEASURABLE FLOWS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS[J]. 数学物理学报(英文版), 2018, 38(1): 157-168.
[5]	刘俊峰, Ciprian A. TUDOR. STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE: EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY[J]. 数学物理学报(英文版), 2017, 37(6): 1545-1566.
[6]	Nguyen Van THIN. NORMAL FAMILY OF MEROMORPHIC FUNCTIONS SHARING HOLOMORPHIC FUNCTIONS AND THE CONVERSE OF THE BLOCH PRINCIPLE[J]. 数学物理学报(英文版), 2017, 37(3): 623-656.
[7]	贾晓菁, 贾仁安. IMPROVE EFFICIENCY OF BIOGAS FEEDBACK SUPPLY CHAIN IN RURAL CHINA[J]. 数学物理学报(英文版), 2017, 37(3): 768-785.
[8]	Shulin LYU, Yang CHEN. THE LARGEST EIGENVALUE DISTRIBUTION OF THE LAGUERRE UNITARY ENSEMALE[J]. 数学物理学报(英文版), 2017, 37(2): 439-462.
[9]	王珺, 陈宗煊. LIMITING DIRECTIONS OF JULIA SETS OF ENTIRE SOLUTIONS TO COMPLEX DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2017, 37(1): 97-107.
[10]	高凌云. ON ENTIRE SOLUTIONS OF TWO TYPES OF SYSTEMS OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2017, 37(1): 187-194.
[11]	Mohammed D. KASSIM, Khaled M. FURATI, Nasser-eddine TATAR. NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS[J]. 数学物理学报(英文版), 2017, 37(1): 119-130.
[12]	马和平, 刘斌. EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY[J]. 数学物理学报(英文版), 2017, 37(1): 235-258.
[13]	Yaghoub JALILIAN. FRACTIONAL INTEGRAL INEQUALITIES AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(5): 1317-1330.
[14]	王珺, 陈宗煊. LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(5): 1331-1342.
[15]	刘玉记. PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS[J]. 数学物理学报(英文版), 2016, 36(5): 1492-1508.