AAM  >> Vol. 4 No. 3 (August 2015)

    Four Types of Functions Solutions of the Novel Auxiliary Equation and Its Application on the Perturbed Nonlinear Schro¨dinger Equation

  • 全文下载: PDF(300KB) HTML   XML   PP.217-223   DOI: 10.12677/AAM.2015.43027  
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刘学,陈怀堂:临沂大学,山东 临沂,山东师范大学,山东 济南

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



Four types of functions solutions of this novel auxiliary equation are gained. We obtain interaction solutions of nonlinear Schrödinger equation with perturbed terms successfully.

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


[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.