构造非线性发展方程无穷序列类孤子精确解的一种方法

套格图桑; 白玉梅

doi:10.7498/aps.61.130202

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摘要

辅助方程法已构造了非线性发展方程的有限多个新精确解. 本文为了构造非线性发展方程的无穷序列类孤子精确解, 分析总结了辅助方程法的构造性和机械化性特点. 在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bcklund变换. 选择了非线性发展方程的两种形式解,借助符号计算系统 Mathematica,用改进的(2+1) 维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解. 这些解包括无穷序列光滑类孤子解, 紧孤立子解和尖峰类孤立子解.

关键词:

作者及机构信息

套格图桑^{1 2},
白玉梅¹

1.
内蒙古民族大学数学学院, 通辽 028043;

2.
内蒙古师范大学数学科学学院, 呼和浩特 010022

基金项目: 国家自然科学基金资助项目(批准号: 10862003)、内蒙古自治区高等学校科学研究基金(批准号: NJZY12031)和内蒙古自治区自然科学基金(批准号: 2010MS0111)资助的课题.

参考文献

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[6]	Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
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[9]	Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[10]
[11]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
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[13]	Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[14]	Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
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[16]	Xie F D,Yuan Z T 2005 Commun. Theor. Phys. (Beijing) 43 39
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[18]	Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 647
[19]
[20]
[21]	LU Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[22]	Xie F D, Gao X S 2004 Commun. Theor. Phys.(Beijing) 41 353
[23]
[24]
[25]	Chen Y, Li B 2004 Commun. Theor. Phys. (Beijing) 41 1
[26]	Ma S H, Fang J P, Zhu H P 2007 Acta Phys. Sin. 56 4319 (in Chinese) [马松华, 方建平, 朱海平 2007 物理学报 56 4319]
[27]
[28]	Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华, 吴小红, 方建平, 郑春龙 2008 物理学报 57 11]
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[30]
[31]	Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569(in Chinese)[李德生, 张鸿庆 2003 物理学报 52 1569]
[32]	Li D S, Zhang H Q 2004 Chin. Phys. 13 984
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[34]	Wang Z,Li D S, Lu H F, Zhang H Q 2005 Chin. Phys. 14 2158
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[36]	Wang Z, Zhang H Q 2006 Chin. Phys. 15 2210
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[40]
[41]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[42]	Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617(in Chinese)[卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]
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[44]	Boiti M 1987 Inverse Problems 3 37
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[50]	Radha R, Lakshmanan M 1999 Chaos, Solitons Fractals 10 1821
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施引文献

[1]	Fan E G 2000 Phys. Lett. A 277 212
[2]
[3]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[4]
[5]	Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin. Phys. 12 1
[6]	Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[7]
[8]
[9]	Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[10]
[11]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[12]
[13]	Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[14]	Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[15]
[16]	Xie F D,Yuan Z T 2005 Commun. Theor. Phys. (Beijing) 43 39
[17]
[18]	Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 647
[19]
[20]
[21]	LU Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[22]	Xie F D, Gao X S 2004 Commun. Theor. Phys.(Beijing) 41 353
[23]
[24]
[25]	Chen Y, Li B 2004 Commun. Theor. Phys. (Beijing) 41 1
[26]	Ma S H, Fang J P, Zhu H P 2007 Acta Phys. Sin. 56 4319 (in Chinese) [马松华, 方建平, 朱海平 2007 物理学报 56 4319]
[27]
[28]	Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华, 吴小红, 方建平, 郑春龙 2008 物理学报 57 11]
[29]
[30]
[31]	Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569(in Chinese)[李德生, 张鸿庆 2003 物理学报 52 1569]
[32]	Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[33]
[34]	Wang Z,Li D S, Lu H F, Zhang H Q 2005 Chin. Phys. 14 2158
[35]
[36]	Wang Z, Zhang H Q 2006 Chin. Phys. 15 2210
[37]
[38]
[39]	Li D S, Zhang H Q 2006 Acta Phys. Sin. 55 1565(in Chinese) [李德生, 张鸿庆 2006 物理学报 55 1565]
[40]
[41]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[42]	Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617(in Chinese)[卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]
[43]
[44]	Boiti M 1987 Inverse Problems 3 37
[45]
[46]	Durovsky V G, Konopelchenko E G 1994 Phys. A 27 4619
[47]
[48]	Radha R, Lakshmanan M 1997 Math. Phys. 38 292
[49]
[50]	Radha R, Lakshmanan M 1999 Chaos, Solitons Fractals 10 1821
[51]

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构造非线性发展方程无穷序列类孤子精确解的一种方法

1. 内蒙古民族大学数学学院, 通辽 028043;

2. 内蒙古师范大学数学科学学院, 呼和浩特 010022

基金项目:

国家自然科学基金资助项目(批准号: 10862003)、内蒙古自治区高等学校科学研究基金(批准号: NJZY12031)和内蒙古自治区自然科学基金(批准号: 2010MS0111)资助的课题.

收稿日期: 2011-10-14

修回日期: 2011-12-08

刊出日期: 2012-07-05

摘要: 辅助方程法已构造了非线性发展方程的有限多个新精确解. 本文为了构造非线性发展方程的无穷序列类孤子精确解, 分析总结了辅助方程法的构造性和机械化性特点. 在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bcklund变换. 选择了非线性发展方程的两种形式解,借助符号计算系统 Mathematica,用改进的(2+1) 维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解. 这些解包括无穷序列光滑类孤子解, 紧孤立子解和尖峰类孤立子解.

关键词:

A method of constructing infinite sequence soliton-like solutions of nonlinear evolution equations

1.
The College of Mathematical, Inner Mongolia University for Nationalities, Tongliao 028043, China;

2.
The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

Fund Project:

Project supported by the National Natural Science Foundation of China(Grant No. 10862003), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China(Grant No. NJZY12031) and the Natural Science Foundation of Inner Mongolia Autonomous Region, China(Grant No. 2010MS0111).

Received Date: 14 October 2011

Accepted Date: 08 December 2011

Published Online: 05 July 2012

Abstract: The auxiliary equation method is used to construct the finite new exact solutions of nonlinear evolution equations. To search for infinite sequence soliton-like exact solutions of nonlinear evolution equations, characteristics of constructivity and mechanization of auxiliary equation method are analyzed and summarized. Therefore, the quasi-Bcklund transformation between new solutions of a kind of auxiliary equation with Riccati equation is presented, then (2+1)-dimensional modified dispersive water-wave system is taken as an applicable example to find infinite sequence soliton-like new exact solutions by choosing two kinds of formal solutions of nonlinear evolution equations with the help of symbolic computation system Mathematica, where included are the infinite sequence smooth soliton-like solutions, compact soliton solutions and peak soliton-like solutions.

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