应用改进的试探函数法求非线性数学物理方程精确解

J4 ›› 2016, Vol. 33 ›› Issue (4): 444-450.

应用改进的试探函数法求非线性数学物理方程精确解

杨娟,冯庆江

凯里学院数学科学学院，贵州凯里 556000

收稿日期:2016-02-20 修回日期:2016-03-23 出版日期:2016-07-28 发布日期:2016-07-28
通讯作者: 杨娟（1982-），女，湖南邵阳人，硕士，讲师，研究方向为非线性数学物理方程。 E-mail:hnyangjuan1982@sohu.com

Exact solutions of nonlinear mathematical physics equations with improved trial function method

Received:2016-02-20 Revised:2016-03-23 Published:2016-07-28 Online:2016-07-28

摘要/Abstract

摘要： 应用改进的试探函数法求得Jimbo-Miwa方程和非线性传输线电位方程的精确解，这些解包括双曲函数解、三角函数解。当对双曲函数解中的参数取特殊值时，可以得到了孤立波解。当对三角函数解中的参数取特殊值时，可以得到对应的周期波函数解。实践证明，试探函数法对于研究非线性数学物理方程具有非常广泛的应用意义。

Abstract: Exact solution for Jimbo-Miwa equation and nonlinear transmission line equation are obtained by means of the trial function method. These solutions include hyperbolic function solutions, trigonometric function solutions. When the arbitrary parameters in hyperbolic function solutions are taken as some special values, the solitary wave solutions can be obtained.When the arbitrary parameters in trigonometric function solutions are taken as some special values, the trigonometric function solutions can be expressed as periodic wave solutions. Experience has proved that trial function method has a very wide range of application in the study of nonlinear mathematical physics equations.

Key words: exact soltions

中图分类号:

O175.2

杨娟冯庆江. 应用改进的试探函数法求非线性数学物理方程精确解[J]. J4, 2016, 33(4): 444-450.

参考文献

[1] Yang lijuan,Yang Qiongfen,Du Xianyun.New exact solutions of Broer-Kaup-Kupershmidt equation[J].Chinese Journal of Quantum Electronics(量子电子学报)，2012,29（2）：142-146.(in Chinese)
[2] Wang Ling,Xan Daquan.Homoclinic breather-wave solutions,periodic-wave solutions and kink solitary-wave solutions for CDGKS equations[J].Chinese Journal of Quantum Electronics(量子电子学报)，2012,29（4）：417-420. (in Chinese)
[3] Zhang Yingyuan,Liu Xiqiang,Wang Gangwei.Symmetry reductions and explicit solutions of (2+1)-dimensional nonlinear evolution equation[J].Chinese Journal of Quantum Electronics(量子电子学报)，2012,29(4):411-416(in Chinese)
[4]. Qiu Chun,Diao Mingjun,Xu Lanlan,et al.A new algebra method for constructing exact solutions of nonlinear evolution equations[J].Chinese Journal of Quantum Electronics(量子电子学报)，2011,29(3):279-285. (in Chinese)
[5] Sun Jian,Narenmandula.Multiple solitary wave solutions of variable coefficient forced Burgers equation and interaction of solitary waves[J].Chinese Journal of Quantum Electronics(量子电子学报)，2011,28(1):31-35. (in Chinese)
[6] Xiao Yafeng,Xue Haili,Zhang Hongqing.New multi-order envelope periodic solutions to cubic nonlinear Schrodinger equation[J].Chinese Journal of Quantum Electronics(量子电子学报)，2012,29(3):269-278(in Chinese)
[7] Han Yuanchun,Erduncang,Narenmandula.Exact solutions and special solitary wave structures for variable coefficients (2+1)-dimensional Burgers system [J]. Chinese Journal of Quantum Electronics(量子电子学报)，2012，29（3）：286-291(in Chinese)
[8] Taogetusang,Yi Lina.New soliton-like solution of generalized Zakharov-Kuzentsov equation [J].Chinese Journal of Quantum Electronics(量子电子学报)，2015,32(3):290-300(in Chinese)
[9] Xiao Yafeng,Xue Haili,Zhang Hongqing.New multi-order envelope periodic solutions to cubic nonlinear Schrodinger equation[J].Chinese Journal of Quantum Electronics(量子电子学报)，2012,29(3):269-278(in Chinese)
[10] Zhuang Binxian,Guo Jun,Xiang Yuanjiang.Bright and dark solitons in metamaterials obtained by extended F-expansion method[J].Acta Physica Sinica (物理学报)，2013,62（5）：0542071-0542079(in Chinese)
[11] Lin Fuzhong,Ma Songhua.New exact solutions and complex wave excitations for the (2+1)-dimensional dispersive long wave equation[J].Acta Physica Sinica (物理学报)，2013,62（5）：0405081-0405087(in Chinese)
[12] Guo Peng,Zhang Lei,Wang Xiaoyun.Explicit and exact solutions to the mBBM and Vakhnenko equations[J].Chinese Journal of Quantum Electronics(量子电子学报)，2010,27(6):683-687(in Chinese)
[13] Feng Qingjiang,Xiao Shaoju.Derivation of exact solutions for Zakharov equation with extended expansion method [J].Chinese Journal of Quantum Electronics(量子电子学报)，2015，32（1）：40-45 (in Chinese)

[1]	马志民1，*，孙峪怀2，. 立方非线性Schr\"{o}dinger方程新精确解[J]. 量子电子学报, 2019, 36(4): 416-422.
[2]	李英杰智红燕. 变系数薛定谔方程的Painlevé分析及解析解[J]. J4, 2017, 34(6): 682-690.
[3]	套格图桑. 首次积分与(n+1)维多重sine-Gordon方程的无穷序列新解[J]. J4, 2017, 34(3): 316-326.
[4]	张小媛许晓革孟祥花. Bell多项式在变系数Gardner-KP方程中的应用[J]. J4, 2016, 33(6): 671-679.
[5]	王晓利斯仁道尔吉. Exp-展开法与变系数非线性发展方程的精确解[J]. J4, 2016, 33(6): 680-688.
[6]	王晓民苏道毕力格. 两个非线性方程的势对称及其不变解[J]. J4, 2016, 33(5): 537-544.
[7]	郝鑫星李彪. 广义变系数(3+1)-维非线性薛定谔方程的有限对称群解[J]. J4, 2016, 33(3): 263-278.
[8]	李凯辉刘汉泽. Lie symmetry analysis and exact solutions for nonlinear LC circuit equation[J]. J4, 2016, 33(3): 279-286.
[9]	杨娟冯庆江. 应用改进的简单方程法求(2+1)维ZK-MEW方程的精确解[J]. J4, 2016, 33(3): 287-291.
[10]	李宁,套格图桑. (2+1)维一般Calogero-Bogoyavlenskii-Schiff系统的无穷序列类孤子新解[J]. J4, 2015, 32(4): 414-418.
[11]	冯庆江肖绍菊. 应用改进的G展开法求Zakharov方程的行波解[J]. J4, 2015, 32(1): 40-45.
[12]	冯春明，刘庆松. 含色散项的Zabolotskaya-Khokhlov方程的对称、约化、精确解和守恒律[J]. J4, 2015, 32(1): 46-52.
[13]	孟祥花许瑞麟许晓革. 广义变系数Burgers-Kadomtsev-Petviashvili方程的自B?cklund变换和精确解析解[J]. J4, 2014, 31(6): 663-669.
[14]	于兴江. （3+1）维广义KdV-Zakharov-Kuznetsev方程的对称、约化和精确解[J]. J4, 2014, 31(6): 670-677.
[15]	阿如娜，套格图桑. 一维Tonks-Girardeau原子气区域中Gross-Pitaevskii方程简化模型的无穷序列新解 [J]. J4, 2014, 31(5): 541-546.