薛定谔扰动耦合系统孤波的行波近似解法

许永红; 韩祥临; 石兰芳; 莫嘉琪

doi:10.7498/aps.63.090204

摘要

研究了一类薛定谔非线性耦合系统. 利用精确解与近似解相关联的特殊技巧，首先讨论了对应的无扰动耦合系统，利用投射法得到了精确的孤波解. 再利用泛函映射方法得到了薛定谔非线性扰动耦合系统的行波近似解.

关键词:

薛定谔系统 /
孤波 /
渐近解

A class of the Schrödinger nonlinear disturbed coupled system is studied, using the specific technique to relate the exact and approximate solutions. Firstly, the corresponding non-disturbed coupled system is considered. The exact solitary wave solution is obtained by using the projection method. Then, the traveling wave approximation solution to the Schrödinger disturbed coupled system is found by using a functional mapping method.

Keywords:

Schrö /
dinger system /
solitary wave

作者及机构信息

1.
蚌埠学院数理系, 蚌埠 233030;

2.
湖州师范学院, 湖州 313000;

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：11202106）、安徽高校省级自然科学研究项目（批准号：KJ2013B003）、浙江省自然科学基金（批准号：LY13A010005）和江苏省自然科学基金项目（批准号：13KJB170016）资助的课题.

Authors and contacts

1.
Department of Mathematics & Physics, Bengbu College, Bengbu 233030, China;

2.
Huzhou Teachers College, Huzhou 313000, China;

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

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

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11202106), the Natural Science Foundation from the Education Bureau of Anhui Province, China (Grant No. KJ2013B003), the Natural Science Foundation of Zhejiang Province, China (Grant No. LY13A010005), and the Natural Sciences Foundation from the Universities of Jiangsu Province, China (Grant No. 13KJB170016).

参考文献

[1]	Parkes E J, Duffy B R, Abbott P C 2008 Chaos Solitons Fractals 38 154
[2]	Sirendaoreji J S 2003 Phys. Lett. A 309 387
[3]	McPhaden M J, Zhang D 2002 Nature 415 603
[4]	Pan L X, Zhuo W M, Yan J R 2005 Acta. Phys. Sin. 54 1 (in Chinese) [潘留仙, 左伟明, 颜家壬 2005 54 1]
[5]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta. Phys. Sin. 50 606 (in Chinese) [封国林, 戴兴刚, 王爱慧, 丑纪范 2001 50 606]
[6]	Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York: CRC Press Co)
[7]	He J H, Wu X H 2006 Chaos Solitions & Fractals 29 108
[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, Teixeira M A 2002 J. Dyn. Differ. Equations 19 309
[11]	Guarguaglini F R, Natalini R 2007 Commun. Partial Differ. Equations 32 163
[12]	Xu Y H, Wen Z H, Mo J Q 2011 Acta. Phys. Sin. 60 050205 (in Chinese) [许永红, 温朝晖, 莫嘉琪 2011 60 050205]
[13]	Xu Y H, Yao J S, Mo J Q 2012 Acta. Phys. Sin. 61 020202 (in Chinese) [许永红, 姚静荪, 莫嘉琪 2012 61 020202]
[14]	Han X L 2004 Acta Phys. Sin. 53 4061 (in Chinese) [韩祥临 2004 53 4061]
[15]	Han X L, Zhao Z J, Cheng R J, Mo J Q 2013 Acta. Phys. Sin. 62 110202 (in Chinese) [韩祥临, 赵振江, 程荣军, 莫嘉琪 2013 62 110202]
[16]	Shi L F, Mo J Q 2013 Acta. Phys. Sin. 62 040203 (in Chinese) [石兰芳, 莫嘉琪 2013 62 040203]
[17]	Shi L F, Lin W T, Lin Y H, Mo J Q 2013 Acta. Phys. Sin. 62 010201 (in Chinese) [石兰芳, 林万涛, 林一骅, 莫嘉琪 2013 62 010201]
[18]	Shi L F, Ouyang C, Chen L H, Mo J Q 2012 cta. Phys. Sin. 61 050203 (in Chinese) [石兰芳, 欧阳成, 陈丽华, 莫嘉琪 2012 61 050203]
[19]	Mo J Q 1989 Science in China, Ser A 32 1306
[20]	Mo J Q 2009 Science in China, Ser G 39 568
[21]	Jmo J Q, Chen X F 2010 Acta. Phys. Sin. 50 1403 (in Chinese) [莫嘉琪, 陈贤峰 2010 50 1403]
[22]	Mo J Q, Lin S R 2009 Chin. Phys. B 18 3628
[23]	Mo J Q 2011 Commun. Theor. Phys. 55 387
[24]	Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203
[25]	Ma S H, Fang J P 2006 Acta. Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 65 5611]
[26]	Li B Q, Ma Y L, Xu M P, Li Y 2011 Acta. Phys. Sin. 60 060203 (in Chinese) [李帮庆, 马玉兰, 徐美萍, 李阳 2011 60 060203]
[27]	Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[28]	de Jager E M, Jiang Furu 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing)

施引文献

[1]	Parkes E J, Duffy B R, Abbott P C 2008 Chaos Solitons Fractals 38 154
[2]	Sirendaoreji J S 2003 Phys. Lett. A 309 387
[3]	McPhaden M J, Zhang D 2002 Nature 415 603
[4]	Pan L X, Zhuo W M, Yan J R 2005 Acta. Phys. Sin. 54 1 (in Chinese) [潘留仙, 左伟明, 颜家壬 2005 54 1]
[5]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta. Phys. Sin. 50 606 (in Chinese) [封国林, 戴兴刚, 王爱慧, 丑纪范 2001 50 606]
[6]	Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York: CRC Press Co)
[7]	He J H, Wu X H 2006 Chaos Solitions & Fractals 29 108
[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, Teixeira M A 2002 J. Dyn. Differ. Equations 19 309
[11]	Guarguaglini F R, Natalini R 2007 Commun. Partial Differ. Equations 32 163
[12]	Xu Y H, Wen Z H, Mo J Q 2011 Acta. Phys. Sin. 60 050205 (in Chinese) [许永红, 温朝晖, 莫嘉琪 2011 60 050205]
[13]	Xu Y H, Yao J S, Mo J Q 2012 Acta. Phys. Sin. 61 020202 (in Chinese) [许永红, 姚静荪, 莫嘉琪 2012 61 020202]
[14]	Han X L 2004 Acta Phys. Sin. 53 4061 (in Chinese) [韩祥临 2004 53 4061]
[15]	Han X L, Zhao Z J, Cheng R J, Mo J Q 2013 Acta. Phys. Sin. 62 110202 (in Chinese) [韩祥临, 赵振江, 程荣军, 莫嘉琪 2013 62 110202]
[16]	Shi L F, Mo J Q 2013 Acta. Phys. Sin. 62 040203 (in Chinese) [石兰芳, 莫嘉琪 2013 62 040203]
[17]	Shi L F, Lin W T, Lin Y H, Mo J Q 2013 Acta. Phys. Sin. 62 010201 (in Chinese) [石兰芳, 林万涛, 林一骅, 莫嘉琪 2013 62 010201]
[18]	Shi L F, Ouyang C, Chen L H, Mo J Q 2012 cta. Phys. Sin. 61 050203 (in Chinese) [石兰芳, 欧阳成, 陈丽华, 莫嘉琪 2012 61 050203]
[19]	Mo J Q 1989 Science in China, Ser A 32 1306
[20]	Mo J Q 2009 Science in China, Ser G 39 568
[21]	Jmo J Q, Chen X F 2010 Acta. Phys. Sin. 50 1403 (in Chinese) [莫嘉琪, 陈贤峰 2010 50 1403]
[22]	Mo J Q, Lin S R 2009 Chin. Phys. B 18 3628
[23]	Mo J Q 2011 Commun. Theor. Phys. 55 387
[24]	Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203
[25]	Ma S H, Fang J P 2006 Acta. Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 65 5611]
[26]	Li B Q, Ma Y L, Xu M P, Li Y 2011 Acta. Phys. Sin. 60 060203 (in Chinese) [李帮庆, 马玉兰, 徐美萍, 李阳 2011 60 060203]
[27]	Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[28]	de Jager E M, Jiang Furu 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing)

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