Chin. Phys. Lett.  2014, Vol. 31 Issue (07): 070201    DOI: 10.1088/0256-307X/31/7/070201
GENERAL |
Dressed Dark Solitons of the Defocusing Nonlinear Schr?dinger Equation
LOU Sen-Yue1,2, CHENG Xue-Ping3, TANG Xiao-Yan3
1Faculty of Science, Ningbo University, Ningbo 315211
2Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062
3Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240
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LOU Sen-Yue, CHENG Xue-Ping, TANG Xiao-Yan 2014 Chin. Phys. Lett. 31 070201
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Abstract The nonlinear Schr?dinger equation is proved to be consistent-tanh-expansion (CTE) solvable. Some types of dark soliton solutions dressed by cnoidal periodic waves are obtained by means of the CTE method.
Published: 30 June 2014
PACS:  02.30.Ik (Integrable systems)  
  42.65.Tg (Optical solitons; nonlinear guided waves)  
  05.45.Yv (Solitons)  
  47.35.Fg (Solitary waves)  
  52.35.Sb (Solitons; BGK modes)  
  47.35.Lf (Wave-structure interactions)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/31/7/070201       OR      https://cpl.iphy.ac.cn/Y2014/V31/I07/070201
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LOU Sen-Yue
CHENG Xue-Ping
TANG Xiao-Yan
[1] Sulem C and Sulem P L 1999 The Nonlinear Schr?dinger Equation-Self-Focusing and Wave Collapse (New York: Springer-Verlag)
Kevrekidis P G 2009 Discrete Nonlinear Sch?dinger Equation-Mathematical Analysis, Numerical Computations and Physical Perspectives (Heidelberg: Springer-Verlag)
[2] Hirota R 1971 Phys. Rev. Lett. 27 1192
Hietarinta J 1987 J. Math. Phys. 28 1732
Hietarinta J 1987 J. Math. Phys. 28 2094
Hietarinta J 1987 J. Math. Phys. 28 2586
Hietarinta J 1988 J. Math. Phys. 29 628
Hu X B and Wang H Y 2006 Inverse Probl. 22 1903
[3] Gu C H et al 2005 Darboux Transformations in Integrable Systems Theory and their Applications to Geometry (Dordrecht: Springer) vol 26
Rogers C and Schief W K 2002 B?cklund and Darboux Transformations Geometry and Modern Applications in Soliton Theory (Cambridge: Cambridge University Press)
[4] Shin H J 2005 Phys. Rev. E 71 036628
Shin H J 2004 J. Phys. A: Math. Gen. 37 8017
Shin H J 2004 arXiv:nlin/0410065v2[nlin.SI]
[5] Egorowa I et al 2009 Math. Nachr. 282 526
[6] Weiss J et al 1983 J. Math. Phys. 24 522
Conte R 1989 Phys. Lett. A 140 383
Lou S Y 1998 Z. Naturforsch. 53a 251
[7] Chen C L and Lou S Y 2013 Chin. Phys. Lett. 30 110202
[8] Lou S Y 2013 arXiv:1308.5891[nlin.SI]
[9] Cheng X P et al 2014 Phys. Rev. E 89 043202
[10] Qiao Z J 2001 Theor. Math. Phys. 127 827
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