新辅助方程的四类函数解对带扰动项非线Schro¨dinger方程的应用
Four Types of Functions Solutions of the Novel Auxiliary Equation and Its Application on the Perturbed Nonlinear Schro¨dinger Equation
DOI: 10.12677/AAM.2015.43027, PDF,    科研立项经费支持
作者: 刘学*, 陈怀堂*：临沂大学，山东 临沂，山东师范大学，山东 济南
关键词: 四类函数解；新辅助方程；相互作用解；Four Types of Functions Solution； Novel Auxiliary Equation Method； Interaction Solution
摘要: 本文通过构造法求解新辅助方程的四类函数解，并将新辅助方程方法带扰动项非线性Schrödinger方程中，成功获得方程的相互作用解。
Abstract: Four types of functions solutions of this novel auxiliary equation are gained. We obtain interaction solutions of nonlinear Schrödinger equation with perturbed terms successfully.
文章引用：刘学, 陈怀堂. 新辅助方程的四类函数解对带扰动项非线Schro¨dinger方程的应用[J]. 应用数学进展, 2015, 4(3): 217-223. http://dx.doi.org/10.12677/AAM.2015.43027

参考文献

[1] Hu, X.B. and Ma, W.X. (2002) Application of Hirota’s bilinear formalism to the Toeplitz lattice—some special soliton- like solutions. Physics Letters A, 293, 161-165. http://dx.doi.org/10.1016/S0375-9601(01)00850-7 [Google Scholar] [CrossRef] 
[2] 谷超豪 (1999) 孤立子理论中的Darboux 变换及其几何应用. 上海科技出版社, 上海.
[3] Geng, X.G. and He, G.L. (2010) Some new integrable nonlinear evolution equations and Darboux transformation. Journal of Mathematical Physics, 51, Article ID: 033514. http://dx.doi.org/10.1063/1.3355192 [Google Scholar] [CrossRef] 
[4] Zhao, Y.L., Liu, Y.P. and Li, Z.B. (2010) A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation. Chinese Physics B, 19, Article ID: 030306.
[5] Chen, H.T. and Yin, H.C. (2007) Double elliptic equation method and new exact solutions of the (n+1)-dimensional sinh-Gordon equation. Journal of Mathematical Physics, 48, Article ID: 013504. http://dx.doi.org/10.1063/1.2424550 [Google Scholar] [CrossRef] 
[6] El-Wakil, S.A., Abulwafa, E.M., Elhanbaly, A. and Abdou, M.A. (2007) The extended homogeneous balance method and its applications for a class of nonlinear evolution equations. Chaos, Solitons & Fractals, 33, 1512-1522. http://dx.doi.org/10.1016/j.chaos.2006.03.010 [Google Scholar] [CrossRef] 
[7] Chen, Y. and Li, B. (2004) General projective Riccati equation method and exact solutions for generalized KdV-type and KdV-Burgers-type equations with nonlinear terms of any order. Chaos, Solitons & Fractals, 19, 977-984. http://dx.doi.org/10.1016/S0960-0779(03)00250-9 [Google Scholar] [CrossRef] 
[8] Chen, H.T., Yang, S.H. and Ma, W.X. (2013) Double sub-equation method for complexiton solutions of nonlinear partial differential equations. Applied Mathematics and Computation, 219, 4775-4781. http://dx.doi.org/10.1016/j.amc.2012.10.094 [Google Scholar] [CrossRef] 
[9] Tang, Y.N., Ma, W.X., Xu, W. and Gao, L. (2011) Wronskian determinant solutions of the (3+1)-dimensional Jimbo- Miwa equation. Applied Mathematics and Computation, 217, 8722-8730. http://dx.doi.org/10.1016/j.amc.2011.03.120 [Google Scholar] [CrossRef] 
[10] Wang, M.L., Li, X.Z. and Zhang, J.L. (2008) The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A, 372, 417-423. http://dx.doi.org/10.1016/j.physleta.2007.07.051 [Google Scholar] [CrossRef] 
[11] 高美茹, 陈怀堂 (2012) (2+1)维sine-Gordon方程的三种函数混合的相互作用解. 物理学报, 22, 138-141.
[12] 徐兰兰, 陈怀堂 (2013) 变系数(2+1)维Nizhnik-Novikov-Vesselov方程的三孤子新解. 物理学报, 9, 090204.
[13] Abdel Latif, M.S. (2014) Bright and dark soliton solutions for the perturbed nonlinear Schrödinger’s equation with Kerr law and non-Kerr law nonlinearity. Applied Mathematics and Computation, 247, 501-510. http://dx.doi.org/10.1016/j.amc.2014.08.098 [Google Scholar] [CrossRef] 

为你推荐