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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.
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Keywords:
- Schrö /
- dinger system /
- solitary wave
[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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[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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