(2+1)维AKNS方程的对称约化和新的非行波精确解

J4 ›› 2013, Vol. 30 ›› Issue (6): 678-683.

(2+1)维AKNS方程的对称约化和新的非行波精确解

康晓蓉,鲜大权

西南科技大学理学院,四川绵阳 621010

收稿日期:2013-06-20 修回日期:2013-07-15 出版日期:2013-11-28 发布日期:2013-11-13
作者简介:康晓蓉 ( 1970 - ),四川汉源人,讲师,研究方向为可积系统理论与应用。
基金资助:
四川省教育厅重点科研基金(10ZA021)、国家自然科学基金(10971169)和国家自然科学基金与中物院联合基金(11076015)资助项目

Symmetry reduction and new non-traveling wave solutions of (2+1)-dimensional AKNS equation

KANG Xiao-rong,XIAN Da-quan

School of Sciences, Southwest University of Science and
Technology, Mianyang 621010, China

Received:2013-06-20 Revised:2013-07-15 Published:2013-11-28 Online:2013-11-13

摘要/Abstract

摘要：

利用Lie群方法将(2+1)维AKNS方程约化成(1+1)维非线性偏微分方程。对约化方程应用扩展同宿测试法获得了AKNS方程的一些新的非行波精确解,这些结果丰富了该方程的可积性内涵及(2+1)维非线性波传播的动力学行为。

关键词: 非线性方程, (2+1)维AKNS方程, Lie群方法, 扩展同宿测试法, 非行波精确解

Abstract:

The (2+1)-dimensional AKNS equation was reduced to (1+1)-dimensional nonlinear partial differential equation by applying the Lie group method. As to the reduced equation, some new non-traveling wave exact solutions were obtained with extended homoclinic test approach. These results enrich the connotations of integrability of the equation and dynamical behavior of (2+1)-dimensional nonlinear wave propagation.

Key words: nonlinear equation, (2+1)-dimensional AKNS equation, Lie group method, extended homoclinic test method, non-traveling wave exact solutions

中图分类号:

O175.2

康晓蓉,鲜大权. (2+1)维AKNS方程的对称约化和新的非行波精确解[J]. J4, 2013, 30(6): 678-683.

KANG Xiao-rong,XIAN Da-quan. Symmetry reduction and new non-traveling wave solutions of (2+1)-dimensional AKNS equation[J]. J4, 2013, 30(6): 678-683.

参考文献

[1]Wang C J, Dai Zh D and Liang L, Exact three-wave solution for higher dimensional KdV-type equation, Appl. Math. Comput. 2010,216:501-505. [2] Dai Zh D, Xian D Q and Li D L, Homoclinic Breather-Wave with Convective Effect for the (1+1)-Dimen sional Boussinesq Equation, China. Phys. Lett. 2009, 26(4), 040203:1-3. [3] Darvishi M T and Khani F, Numerical and explicit solutions of the fifth-order. Korteweg-de Vries equations, Chaos, Solitons and Fractals, 2009,39:2484–2490. [4] Abbasbandy S and Darvishi M T, A numerical solution of Burgers’ equation by time discretization of Adomian’s decomposition method, Appl. Math. Comput. 2005,170, 95-120. [5] Darvishi M T, Khani F, Hamedi-Nezhad S and Ryu S W, New modification of the HPM for numerical solutions of the sine-Gordon and coupled sine-Gordon equations, Int. J. Comput. Math. 2010, 87: 908-919. [6] Shin B C, Darvishi M T and Karami A , Application of He's parameter-expansion method to a nonlinear self-excited oscillator system, Int.J.Nonlin. Sci. Num. Simul. 2009,10: 137-143. [7] He J H and Abdou M A, New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons and Fractals,2007, 34: 1421-1429. [8] Darvishi M T and Najai M , A Modification of Extended Homoclinic Test Approach to Solve the (3+1)-Dimen sional Potential-YTSF Equation, Chin. Phys. Lett.2011, 28, 040202:1-4. [9] Mohammad N, Maliheh N and Darvishi M T, New Exact Solutions to the (2+1)D AKNS Equation: Modification of the Extended Homoclinic Test Approach, Chin. Phys. Lett. 2012, 29(4), 040202:1-4. [10] Abdul-Majid Wazwaz, The Tanh-coth and the Sine-cosine methods for kinks, solitons, and periodic solutions for the Pochhammer-Chree equations, Appl. Math. Comput. 2008,195: 24-33. [11] Polver P J, Application of Lie Groups to Differential Equations Berlin: Springer; 1986. [12]Wang Ting-ting, Liu Xi-qiang, Yu Jin-qian.Symmetries, exact solutions of and conservation lows of Caudrey-Dodd-Gibbon-Kotera-Sawada equation [J].Chinese Journal of Quantum Electronics (量子电子学报)，2011,28:385-390(in Chinese). [13]Cao Jie,Liu Xiqiang,Guo Meiyu.New solutions and conservation lows of the (3+1)-dimensional nonlinear evolution equations [J].Chinese Journal of Quantum Electronics(量子电子学报)，2009,26:16-22(in Chinese). [14]Xu Bin,et al.Symmetry reduction and invariable solutions of the (2+1)-dimensional Cardner equation [J]Chinese Journal of Quantum Electronics (量子电子学报)，2009,26:531-536(in Chinese). [15] Xian D Q, Chen H L, Symmetry Reduced and New Exact Non-traveling Wave Solutions of Potential Kadomtsev-Petviashvili Equation with p-Power, Appl. Math. Comput. 216(2010)70-79. [16] Wang Ling, Xian Da-quan, Homoclinic Breather-Wave Solutions Periodic-Wave Solutions and Kink Solitary-Wave Solutions for CDGKS Equations, [J].Chinese Journal of Quantum Electronics，2012,29:417-420(in Chinese).