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非线性Schrdinger方程是物理学中具有广泛应用的非线性模型之一. 本文采用相似变换, 将具有色散系数的(2+1)维非线性Schrdinger方程简化成熟知的Schrdinger方程, 进而得到原方程的有理解和一些空间孤子.
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关键词:
- 非线性Schrdinger方程 /
- 相似变换 /
- 有理解 /
- 孤子结构
The nonlinear Schrdinger equation is one of the most important nonlinear models with widely applications in physics. Based on a similarity transformation, the (2+1)-dimensional nonlinear Schrdinger equation with distributed coefficients is transformed into a traceable nonlinear Schrdinger equation, and then two types of rational solutions and several spatial solitons are derived.-
Keywords:
- nonlinear Schrdinger equation /
- similarity transformation /
- rational solution /
- soliton structure
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[2] Dodd R K, Eilbeck J C, Gibbon J D, Morris H C 1982 Solitons and nonlinear wave equations (New York: Academic Press)
[3] Pitaevskii L P, Stringari S 2003 Bose-Einstein Condensation (Oxford: Oxford University Press)
[4] Scott A 1999 Nonlinear Science: Emergence and Dynamics of Coherent Structures (Vol. 1) (Oxford: Oxford University Press)
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[9] Zong F D, Dai C Q, Yang Q, Zhang J F 2006 Acta Phys. Sin. 55 3805 (in Chinese) [宗丰德, 戴朝卿, 杨琴, 张解放 2006 物理学报 55 3805]
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[11] Kruglov V I, Peacock A C, Harvey J D 2005 Phys. Rev. E 71 056619
[12] Zhong W P, Xie R H, Belić M, Petrović N, Chen G, Yi L 2008 Phys. Rev. A 78 023821
[13] Dai C Q, Zhang J F 2010 Opt. Lett. 35 2651
[14] Dai C Q, Zhu S Q, Zhang J F 2010 Opt. Commun. 283 3784
[15] Kruglov V I, Peacock A C, Harvey J D 2003 Phys. Rev. Lett. 90 113902
[16] Chen S H, Dudley J M 2009 Phys. Rev. Lett. 102 233903
[17] Qian C, Wang L L, Zhang J F 2011 Acta Phys. Sin. 60 064214 (in Chinese) [钱存, 王亮亮, 张解放 2011 物理学报 60 064214]
[18] Yan Z Y, Konotop V V, Akhmediev 2010 Phys. Rev. E 82 036610
[19] Akhmediev N, Soto-Crespo J M, Ankiewicz A 2009 Phys. Lett. A 373 2137
[20] Akhmediev N, Ankiewicz A, Soto-Crespo J M 2009 Phys. Rev. E 80 026601
[21] Yan Z Y 2010 Commun. Theor. Phys. (Beijing, China) 54 947
[22] Yan Z Y 2010 Phys. Lett. A 374 672
-
[1] Kivshar Y, Agrawal G P 2003 Optical Solitons: From Fibers to Photonic Crystals (New York: Academic Press)
[2] Dodd R K, Eilbeck J C, Gibbon J D, Morris H C 1982 Solitons and nonlinear wave equations (New York: Academic Press)
[3] Pitaevskii L P, Stringari S 2003 Bose-Einstein Condensation (Oxford: Oxford University Press)
[4] Scott A 1999 Nonlinear Science: Emergence and Dynamics of Coherent Structures (Vol. 1) (Oxford: Oxford University Press)
[5] Zhang J F, Dai C Q, Yang Q, Zhu J M 2005 Opt. Commun. 252 408
[6] Zhao L H, Dai C Q 2010 Eur. Phys. J. D 58 327
[7] Dai C Q, Wang Y Y, Zhang J F 2010 Opt. Express 35 17548
[8] Dai C Q, Wang X G, Zhang J F 2011 Ann. Phys. 326 645
[9] Zong F D, Dai C Q, Yang Q, Zhang J F 2006 Acta Phys. Sin. 55 3805 (in Chinese) [宗丰德, 戴朝卿, 杨琴, 张解放 2006 物理学报 55 3805]
[10] Chen S, Yi L, Guo D S, Lu P 2005 Phys. Rev. E 72 016622
[11] Kruglov V I, Peacock A C, Harvey J D 2005 Phys. Rev. E 71 056619
[12] Zhong W P, Xie R H, Belić M, Petrović N, Chen G, Yi L 2008 Phys. Rev. A 78 023821
[13] Dai C Q, Zhang J F 2010 Opt. Lett. 35 2651
[14] Dai C Q, Zhu S Q, Zhang J F 2010 Opt. Commun. 283 3784
[15] Kruglov V I, Peacock A C, Harvey J D 2003 Phys. Rev. Lett. 90 113902
[16] Chen S H, Dudley J M 2009 Phys. Rev. Lett. 102 233903
[17] Qian C, Wang L L, Zhang J F 2011 Acta Phys. Sin. 60 064214 (in Chinese) [钱存, 王亮亮, 张解放 2011 物理学报 60 064214]
[18] Yan Z Y, Konotop V V, Akhmediev 2010 Phys. Rev. E 82 036610
[19] Akhmediev N, Soto-Crespo J M, Ankiewicz A 2009 Phys. Lett. A 373 2137
[20] Akhmediev N, Ankiewicz A, Soto-Crespo J M 2009 Phys. Rev. E 80 026601
[21] Yan Z Y 2010 Commun. Theor. Phys. (Beijing, China) 54 947
[22] Yan Z Y 2010 Phys. Lett. A 374 672
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