非线性扰动时滞长波系统孤波近似解

汪维刚; 林万涛; 石兰芳; 莫嘉琪

doi:10.7498/aps.63.110204

摘要

本文是讨论一类时滞非线性扰动长波系统的孤波解. 首先，引入非扰动的典型长波方程的精确解. 然后，用同伦映射和改进的技巧构造了非线性扰动时滞长波系统孤波行波解的近似展开式.

关键词:

近似解 /
孤波 /
时滞

The solitary wave approximate solutions for a class of nonlinear-disturbed time delay long-wave system are considered. First, we introduce into exact solution of a non-disturbed typical long-wave system. Then, by using the homotopic mapping and an improved technique, the approximate expansions of the traveling wave solutions for the nonlinear-disturbed time delay long-wave systems are constructed.

Keywords:

作者及机构信息

1.
安庆师范学院桐城教学部, 桐城 231402;

2.
中国科学院大气物理研究所, 大气科学和地球流体力学数值模拟国家重点实验室, 北京 100029;

3.
南京信息工程大学数学与统计学院, 南京 210044;

4.
安徽师范大学数学系, 芜湖 241003

基金项目: 国家自然科学基金（批准号：41275062，11202106）、江苏省高校自然科学研究项目（批准号：13KJB170016）、南京信息工程大学预研基金（批准号：20110385）和安徽高校省级自然科学研究项目（批准号：KJ2013A133）资助的课题.

Authors and contacts

1.
Tongcheng Teaching Department, Anqing Teacher's College, Tongcheng 231402, China;

2.
State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamic, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;

3.
College of Mathematics and Statistics, Nanjing University of information Science and Technology, Nanjing 210044, China;

4.
Department of Mathematics, Anhuii Normal University, Wuhu 241003, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41275062, 11202106), the Natural Sciences Foundation from the Universities of Jiangsu Province, China (Grant No. 13KJB170016), the Advance Research Foundation in NUIST of China (Grant No. 20110385), and the Natural Science Foundation from the Education Bureau of Anhui Province, China (Grant No. KJ2013A133).

参考文献

[1]	Parkes E J 2008 Chaos Solitons Fractals 154
[2]	Wang M L 1995 Phys. Lett. A 199 169
[3]	Sirendaoreji J S 2003 Phys. Lett. A 309 387
[4]	Yang J R, Mao J J 2008 Chin. Phys. Lett. 25 1527
[5]	Yang X D, Ruan H Y, Luo S Y 2007 Commum. Theor. Phys. 48 961
[6]	Yang J R, Mao J J 2008 Chin. Phys. B 17 4337
[7]	Tapgetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 2121 (in Chinese) [套格图桑, 斯仁道尔吉 2009 58 2121]
[8]	Ni W M, Wei J C 2006 J. Differ. Equations 221 158
[9]	Bartier J P 2006 Asymptotic Anal. 46 325
[10]	Libre J, da Silva P R 2007 J. Dyn. Differ. Equations 19 309
[11]	Faye L, Frenod, E, Seck D 2011 Discrete Contin. Dyn. Syst. 29 1001
[12]	Tian C R, Zhu P 2011 Acta Appl. Math. 121 157
[13]	Mo J Q 1989 Science in China Ser A 32 1306
[14]	Han X L, Zhao Z J, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 110203 (in Chinese) [韩祥临, 赵振江, 程荣军, 莫嘉琪 2013 62 110203]
[15]	Mo J Q, Wang H 2007 Acta Ecologica Sinica 27 4366
[16]	Mo J Q, Zhang W J, He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [莫嘉琪, 张伟江, 何铭 2007 56 1843]
[17]	Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese) [莫嘉琪, 张伟江, 陈贤峰 2007 56 6169]
[18]	Shi L F, Lin W T, Lin Y H, Mo J Q 2013 Acta Phys. Sin. 62 010203 (in Chinese) [石兰芳, 林万涛, 林一骅, 莫嘉琪 2013 62 010203]
[19]	Mo J Q, Zhang W J, He M 2006 Acta Phys. Sin. 55 3233 (in Chinese) [莫嘉琪, 张伟江, 何铭 2006 55 3233]
[20]	Shi L F, Ouyang C, Mo J Q 2012 Acta Phys. Sin. 61 120201 (in Chinese) [石兰芳, 欧阳成, 莫嘉琪 2012 61 120201]
[21]	Shi L F, Zhou X C, Mo J Q 2013 Acta Phys. Sin. 62 230202
[22]	Lin W T, Chen L H, Ouyang C, Mo J Q 2012 Acta Phys. Sin. 61 080204 (in Chinese) [林万涛, 陈丽华, 欧阳成, 莫嘉琪 2012 61 080204]
[23]	Lin W T, Lin Y H, Shi L F, Mo J Q 2013 Acta Phys. Sin. 62 140202 (in Chinese) [林万涛, 林一骅, 石兰芳, 莫嘉琪 2013 62 140202]
[24]	Lin W T, Zhang Y, Mo J Q 2013 Chin. Phys. B 22 030205
[25]	Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method, New York, CRC Press Co
[26]	He J H 2002 Approximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese)
[27]	Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems, Basel, Birkhauserm Verlag AG
[28]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑, 斯仁道尔吉 2006 55 3246]

施引文献

[1]	Parkes E J 2008 Chaos Solitons Fractals 154
[2]	Wang M L 1995 Phys. Lett. A 199 169
[3]	Sirendaoreji J S 2003 Phys. Lett. A 309 387
[4]	Yang J R, Mao J J 2008 Chin. Phys. Lett. 25 1527
[5]	Yang X D, Ruan H Y, Luo S Y 2007 Commum. Theor. Phys. 48 961
[6]	Yang J R, Mao J J 2008 Chin. Phys. B 17 4337
[7]	Tapgetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 2121 (in Chinese) [套格图桑, 斯仁道尔吉 2009 58 2121]
[8]	Ni W M, Wei J C 2006 J. Differ. Equations 221 158
[9]	Bartier J P 2006 Asymptotic Anal. 46 325
[10]	Libre J, da Silva P R 2007 J. Dyn. Differ. Equations 19 309
[11]	Faye L, Frenod, E, Seck D 2011 Discrete Contin. Dyn. Syst. 29 1001
[12]	Tian C R, Zhu P 2011 Acta Appl. Math. 121 157
[13]	Mo J Q 1989 Science in China Ser A 32 1306
[14]	Han X L, Zhao Z J, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 110203 (in Chinese) [韩祥临, 赵振江, 程荣军, 莫嘉琪 2013 62 110203]
[15]	Mo J Q, Wang H 2007 Acta Ecologica Sinica 27 4366
[16]	Mo J Q, Zhang W J, He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [莫嘉琪, 张伟江, 何铭 2007 56 1843]
[17]	Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese) [莫嘉琪, 张伟江, 陈贤峰 2007 56 6169]
[18]	Shi L F, Lin W T, Lin Y H, Mo J Q 2013 Acta Phys. Sin. 62 010203 (in Chinese) [石兰芳, 林万涛, 林一骅, 莫嘉琪 2013 62 010203]
[19]	Mo J Q, Zhang W J, He M 2006 Acta Phys. Sin. 55 3233 (in Chinese) [莫嘉琪, 张伟江, 何铭 2006 55 3233]
[20]	Shi L F, Ouyang C, Mo J Q 2012 Acta Phys. Sin. 61 120201 (in Chinese) [石兰芳, 欧阳成, 莫嘉琪 2012 61 120201]
[21]	Shi L F, Zhou X C, Mo J Q 2013 Acta Phys. Sin. 62 230202
[22]	Lin W T, Chen L H, Ouyang C, Mo J Q 2012 Acta Phys. Sin. 61 080204 (in Chinese) [林万涛, 陈丽华, 欧阳成, 莫嘉琪 2012 61 080204]
[23]	Lin W T, Lin Y H, Shi L F, Mo J Q 2013 Acta Phys. Sin. 62 140202 (in Chinese) [林万涛, 林一骅, 石兰芳, 莫嘉琪 2013 62 140202]
[24]	Lin W T, Zhang Y, Mo J Q 2013 Chin. Phys. B 22 030205
[25]	Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method, New York, CRC Press Co
[26]	He J H 2002 Approximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese)
[27]	Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems, Basel, Birkhauserm Verlag AG
[28]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑, 斯仁道尔吉 2006 55 3246]

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