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构造孤子解的新算法及其实现

赵文强 柳银萍

赵文强, 柳银萍. 构造孤子解的新算法及其实现[J]. 华东师范大学学报(自然科学版), 2016, (6): 127-138. doi: 10.3969/j.issn.1000-5641.2016.06.014
引用本文: 赵文强, 柳银萍. 构造孤子解的新算法及其实现[J]. 华东师范大学学报(自然科学版), 2016, (6): 127-138. doi: 10.3969/j.issn.1000-5641.2016.06.014
ZHAO Wen-qiang, LIU Yin-ping. A new algorithm for constructing soliton solution and its implementation[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 127-138. doi: 10.3969/j.issn.1000-5641.2016.06.014
Citation: ZHAO Wen-qiang, LIU Yin-ping. A new algorithm for constructing soliton solution and its implementation[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 127-138. doi: 10.3969/j.issn.1000-5641.2016.06.014

构造孤子解的新算法及其实现

doi: 10.3969/j.issn.1000-5641.2016.06.014
基金项目: 

国家自然科学基金重点项目(11435005)

详细信息
    通讯作者:

    柳银萍, 女, 教授, 博士生导师, 研究方向为符号计算和数学机械化.E-mail: ypliu@cs.ecnu.edu.cn.

A new algorithm for constructing soliton solution and its implementation

  • 摘要: 结合 Painleve 分析, 进一步改进了简单 Hirota 方法. 改进后的算法能够适用于更多方程和方程组. 基于该方法, 在符号计算软件 Maple 平台下研发了软件 ZASP, 将新方法求解非线性演化方程的过程自动化. 通过若干应用实例, 介绍了 ZASP 的使用, 也验证了 ZASP 作为研究非线性演化方程工具的有效性.
  • [1]

    [ 1 ] HIROTA R. Exact soliton of the Korteweg-de Vries equation for multiple collisions of solitons [J]. Physical Review Letters, 1971, 27(18): 1192-1194.
    [ 2 ] SATSUMA J, ABLOWITZ M J. Two-dimensional lumps in nonlinear dispersive systems [J]. Journal of Mathematical Physics, 1979, 20(7): 1496-1503.
    [ 3 ] NAKAMURA A. A direct method of calculating periodic wave solutions to nonlinear evolution equations I: Exact two-periodic wave solution [J]. Journal of the Physical Society of Japan, 1979, 47(5): 1701-1705.
    [ 4 ] NAKAMURA A. A direct method of calculating periodic wave solutions to nonlinear evolution equations II: Exact one-and two-periodicWave solution of the coupled bilinear equations [J]. Journal of the Physical Society of Japan, 1980, 48(4): 1365-1370.
    [ 5 ] HIROTA R, ITO M. Resonance of solitons in one dimension [J]. Journal of the Physical Society of Japan, 1983, 52(3): 744-748.
    [ 6 ] HIETARINT J, HIROTA. Multidromion solutions to the Davey-Stewartson equation [J]. Physics Letters A, 1990, 145(5): 237-244.
    [ 7 ] HIETARINT J. One-dromion solutions for generic classes of equations [J]. Physics Letters A, 1990, 149(2/3): 113-118.
    [ 8 ] HEREMAN W, ZHUANG W. Symbolic computation of solitons with MACSYMA [C]. Journal of Computational and Applied Mathematics II: Differential equations, 1992: 287-296.
    [ 9 ] HEREMAN W, ZHUANG W. A MACSYMA program for the Hirota method [C]//Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics. 1991: 22-26.
    [10] WAZWAZ A M. Solitons and singular solitons for the Gardner-KP equation [J]. Applied Mathematics and Computation, 2008, 204(1): 162-169.
    [11] WAZWAZ A M. Multiple soliton solutions and multiple singular soliton solutions for two integrable systems [J]. Physics Letters A, 2008, 372(46): 6879-6886.
    [12] WAZWAZ A M. Multiple soliton solutions and multiple singular soliton solutions for (2+1)-dimensional shallow water wave equations [J]. Physics Letters A, 2009, 373(33): 2927-2930.
    [13] WAZWAZ A M. Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota’s method, tanh-coth method and Exp-function method [J]. Applied Mathematics and Computation, 2008, 202(1): 275-286.
    [14] WAZWAZ A M. Regular soliton solutions and singular soliton solutions for the modified Kadomtsev-Petviashvili equations [J]. Applied Mathematics and Computation, 2008, 204(1): 227-232.
    [15] WAZWAZ A M. Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations [J]. Applied Mathematics and Computation, 2008, 203(2): 592-597.
    [16] WAZWAZ A M. Multiple soliton solutions for three systems of broer-kaup-kupershmidt equations describing nonlinear and dispersive long gravity waves [J]. Modern Physics Letters B, 2012, 26(20): 3305-3307.
    [17] GILSON C, LAMBERT F, NIMMO J, et al. On the Combinatorics of the Hirota D-operators [J]. Proceedings of the Royal Society A Mathematical Physical & Engineering Sciences, 1996, 452(1945): 223-234.
    [18] LAMBERT F, SPRINGAEL J. Construction of Backlund transformations with binary Bell polynomials [J]. Journal of the Physical Society of Japan, 1997, 66(8): 2211-2213.
    [19] LAMBERT F, LEBLE S, SPRINGAEL J. Binary Bell Polynomials and Darboux covariant Lax pairs [J]. Glasgow Mathematical Journal, 2001, 43(A): 53-63.
    [20] LAMBERT F, SPRINGAEL J. Classical Darboux transformations and the KP hierarchy [J]. Inverse Problems, 2001, 17(4): 1067-1074.
    [21] LAMBERT F, SPRINGAEL J, COLIN S, et al. An elementary approach to hierarchies of soliton equations [J]. Journal of the Physical Society of Japan, 2007, 76(5): 1086-1102.
    [22] LAMBERT F, SPRINGAEL J. Soliton equations and simple combinatorics [J]. Acta Applicandae Mathematicae, 2008, 102(2-3): 147-178.
    [23] FAN E G. Binary Bell polynomials approach to the integrability of nonisospectral and variable-coefficient non-linear equations [J/OL]. arXiv preprint, 2010, 4194(1008): 39-39.http://arxiv.org/abs/1008.4194.
    [24] FAN E G. New bilinear Backlund transformation and Lax pair for the supersymmetric two-Boson equation [J]. Studies in Applied Mathematics, 2011, 127(3): 284-301.
    [25] FAN E G, CHOW W K. Darboux covariant Lax pairs and infinite conservation laws of the (2+1)-dimensional breaking soliton equation [J]. Journal of Mathematical Physics, 2011, 52(2): 023504-023504-10.
    [26] 王红艳, 胡星标. 带自相容源的孤立子方程~[M]. 北京: 清华大学出版社,2008.
    [27] HU X B, WANG D L, TAM W H, et al. Soliton solutions to the Jimbo-Miwa equations and the Fordy-Gibbons-Jimbo-Miwa equation [J]. Physics Letters A, 1999, 262(S4/5): 310-320.
    [28] HU X B, WANG D L, QIAN X M. Soliton solutions and symmetries of the 2+1 dimensional Kaup-Kupershmidt equation [J]. Physics Letters A, 1999, 262(262): 409-415.
    [29] CHEN D Y, ZHANG D J, DENG S F. The novel multi-soliton solutions of the MKdV-Sine Gorden eqations [J]. Journal of the Physical Society of Japan, 2002, 71(2): 658-659.
    [30] CHEN D Y, ZHANG D J, DENG S F. Remarks on some solutions of soliton equations [J]. Journal of the Physical Society of Japan, 2002, 71(8): 2072-2073.
    [31] ZHANG D J, CHEN D Y. The N-soliton solutions of the Sine-Gordon equation with self-consistent sources [J]. Physica A Statistical Mechanics & Its Applications, 2003, 321(3-4): 467-481.
    [32] 周振江. 可积系统孤子解的符号计算研究~[D].上海: 华东师范大学, 2012.
    [33] 张丽. 非线性演化方程孤子解的符号计算研究~[D].上海: 华东师范大学, 2014.
    [34] 杨云青. 可积系统与混沌系统中若干问题的符号计算研究~[D].上海: 华东师范大学, 2011.
    [35] 胡晓瑞. 非线性系统的对称性与可积性~[D]. 上海: 华东师范大学,2012.
    [36] 王云虎. 基于符号计算的可积系统的若干问题研究~[D]. 上海:华东师范大学, 2013.
    [37] 苗倩. 对称优化和Bell多项式的程序算法~[D]. 上海: 华东师范大学,2014.
    [38] 杨铎.Painlevé分析和函数展开法在非线性偏微分方程求解中的应用~[D].浙江宁波: 宁波大学, 2014.
    [39] 徐桂琼. 非线性演化方程的精确解与可积性研究及其符号计算研究~[D].上海: 华东师范大学, 2004.
    [40] 刘山亮, 王文正. 用广田法求扩充的非线性薛定谔方程的精确孤子解~[J].量子电子学报, 1997, 14(2): 144-149.
    [41] 吴妙仙, 王晓芬, 张翼. Hirota方法求解KdV-mKdV混合方程的多孤子解~[J].浙江外国语学院学报, 2008, 3(2): 69-74.

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出版历程
  • 收稿日期:  2015-11-03
  • 刊出日期:  2016-11-25

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