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Search for exact solutions to the generalized nonlinear Schrödinger equation is one of the essential directions in studies of the nonlinear dynamics in optical soliton and Bose-Einstein condensates. Stable soliton modes are of great significance for the experimental realization and potential application. In this paper, based on the introduction of a similarity transformation, the variable-coefficient nonlinear Schrödinger equation is transformed into the nonlinear Schrödinger equation, and then the single soliton solution, two-soliton solution and soliton solution in continuous-wave background for the variable coefficient nonlinear Schrödinger equation are obtained by using the known solutions. Meanwhile, their image analysis and relative discussion are given by selecting the different parameters in detail.
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Keywords:
- Nonlinear Schrödinger equation /
- similarity transformation /
- variable-coefficients /
- soliton solutions /
[1] Thacker H B 1981 Rev. Mod. Phys. 53 253
[2] Bogatyrev V A, Bubnov M M, Dianov E M,Kurkov A S, Mamyshev P V, Prokhorov A M, Rumyantsev S D, Semenov V A, Semenov S L, Sysoliatin A A, Chernikov S V, Guryanov A N, Devyatykh G G, Miroshnichenko S I 1991 J. Lightwave Technol. 9 561
[3] Mamyshev P V, Chers V, Dianov M 1991 IEEE J. Quantum Electron. 7 2347
[4] Taijima K 1987 Opt. Lett. 12 54
[5] Bordon E E, Anderson W L 1989 J. Lightwave Technol. 7 353
[6] Wabnitz S 1996 Opt. Lett. 21 638
[7] Kuehl H H 1988 J. Opt. Soc. Am. B 5 709
[8] Smith N J, Doran N J 1996 Opt. Lett. 21 570
[9] Kivshar Y S, Konotop V V 1989 Sov. J . Quantum Electron. 19 566
[10] Quiroga-Teixeiro M L, Andrekson P A 1996 J. Opt. Soc. Am. B 13 687
[11] Gabitov I R, Turitsyn S K 1996 Opt.Lett. 21 37
[12] Zhang J F, Cheng F Y 2001 Acta Phys. Sin. 50 1648 (in Chinese)[张解放、陈芳跃 2001 50 1648 ]
[13] Lou S Y, Ruan H Y 1992 Acta Phys. Sin. 41 182 (in Chinese)[楼森岳、阮航宇 1992 41 182 ]
[14] Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 1923 (in Chinese)[刘式适、付遵涛、刘式达、赵 强 2002 51 1923 ]
[15] Xu C Z, Zhang J F 2004 Acta Phys. Sin. 53 3652(in Chinese) [徐昌智、张解放 2004 53 3652]
[16] Hao R Y, Lu L, Li Z H 2004 Opt. Commun. 79 236
[17] Li B, Chen Y 2004 Chaos Soliton Fract. 21 241
[18] Kruglov V I, Peacock A C, Harvery J D 2003 Phys. Rev. Lett. 90 11392
[19] Zong F D, Dai C Q, Yang Q, Zhang J F 2006 Acta Phys. Sin. 55 3805 [宗丰德、戴朝卿、杨 琴、张解放 2006 55 3805]
[20] Belmonte-Beitia J, Pérez-García V M, Vekslerchik V,Konotop V V 2008 Phys. Rev. Lett. 100 164102
[21] Belmonte-Beitia J,Cuevas J 2009 J. Phys. A 42 165201
[22] Yan J R 1996 Chin. Sci. Bull. 41 17
[23] Bélanger N, Bélanger P A 1996 Opt. Commun. 124 301
[24] He J S, Ji M,Li Y S 2007 Chin. Phys. Lett. 24 8
[25] Sergey A P,Govind P A 2006 Phys. Rev. Lett. 97 013901
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[1] Thacker H B 1981 Rev. Mod. Phys. 53 253
[2] Bogatyrev V A, Bubnov M M, Dianov E M,Kurkov A S, Mamyshev P V, Prokhorov A M, Rumyantsev S D, Semenov V A, Semenov S L, Sysoliatin A A, Chernikov S V, Guryanov A N, Devyatykh G G, Miroshnichenko S I 1991 J. Lightwave Technol. 9 561
[3] Mamyshev P V, Chers V, Dianov M 1991 IEEE J. Quantum Electron. 7 2347
[4] Taijima K 1987 Opt. Lett. 12 54
[5] Bordon E E, Anderson W L 1989 J. Lightwave Technol. 7 353
[6] Wabnitz S 1996 Opt. Lett. 21 638
[7] Kuehl H H 1988 J. Opt. Soc. Am. B 5 709
[8] Smith N J, Doran N J 1996 Opt. Lett. 21 570
[9] Kivshar Y S, Konotop V V 1989 Sov. J . Quantum Electron. 19 566
[10] Quiroga-Teixeiro M L, Andrekson P A 1996 J. Opt. Soc. Am. B 13 687
[11] Gabitov I R, Turitsyn S K 1996 Opt.Lett. 21 37
[12] Zhang J F, Cheng F Y 2001 Acta Phys. Sin. 50 1648 (in Chinese)[张解放、陈芳跃 2001 50 1648 ]
[13] Lou S Y, Ruan H Y 1992 Acta Phys. Sin. 41 182 (in Chinese)[楼森岳、阮航宇 1992 41 182 ]
[14] Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 1923 (in Chinese)[刘式适、付遵涛、刘式达、赵 强 2002 51 1923 ]
[15] Xu C Z, Zhang J F 2004 Acta Phys. Sin. 53 3652(in Chinese) [徐昌智、张解放 2004 53 3652]
[16] Hao R Y, Lu L, Li Z H 2004 Opt. Commun. 79 236
[17] Li B, Chen Y 2004 Chaos Soliton Fract. 21 241
[18] Kruglov V I, Peacock A C, Harvery J D 2003 Phys. Rev. Lett. 90 11392
[19] Zong F D, Dai C Q, Yang Q, Zhang J F 2006 Acta Phys. Sin. 55 3805 [宗丰德、戴朝卿、杨 琴、张解放 2006 55 3805]
[20] Belmonte-Beitia J, Pérez-García V M, Vekslerchik V,Konotop V V 2008 Phys. Rev. Lett. 100 164102
[21] Belmonte-Beitia J,Cuevas J 2009 J. Phys. A 42 165201
[22] Yan J R 1996 Chin. Sci. Bull. 41 17
[23] Bélanger N, Bélanger P A 1996 Opt. Commun. 124 301
[24] He J S, Ji M,Li Y S 2007 Chin. Phys. Lett. 24 8
[25] Sergey A P,Govind P A 2006 Phys. Rev. Lett. 97 013901
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