Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation

doi:10.1088/1674-1056/22/11/110306

中国物理B ›› 2013, Vol. 22 ›› Issue (11): 110306-110306.doi: 10.1088/1674-1056/22/11/110306

Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation

陈俊超^a, 李彪^b, 陈勇^a

a Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;
b Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

收稿日期:2013-03-16 修回日期:2013-04-24 出版日期:2013-09-28 发布日期:2013-09-28
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11275072, 11075055, and 11271211), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004), the Shanghai Leading Academic Discipline Project, China (Grant No. B412), the National High Technology Research and Development Program of China (Grant No. 2011AA010101), and the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213).

Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation

Chen Jun-Chao (陈俊超)^a, Li Biao (李彪)^b, Chen Yong (陈勇)^a

a Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;
b Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

Received:2013-03-16 Revised:2013-04-24 Online:2013-09-28 Published:2013-09-28
Contact: Chen Yong E-mail:ychen@sei.ecnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11275072, 11075055, and 11271211), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004), the Shanghai Leading Academic Discipline Project, China (Grant No. B412), the National High Technology Research and Development Program of China (Grant No. 2011AA010101), and the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213).

摘要/Abstract

摘要： We construct various novel exact solutions of two coupled dynamical nonlinear Schrödinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrödinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrödinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.

关键词: coupled dynamical nonlinear Schrödinger equations, coupled nonlinear Schrödinger equations with time–space modulation, exact solutions

Abstract: We construct various novel exact solutions of two coupled dynamical nonlinear Schrödinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrödinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrödinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.

Key words: coupled dynamical nonlinear Schrödinger equations, coupled nonlinear Schrödinger equations with time–space modulation, exact solutions

中图分类号:

03.75.-b

05.45.Yv (Solitons) 31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)

陈俊超, 李彪, 陈勇. Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation[J]. 中国物理B, 2013, 22(11): 110306-110306.

Chen Jun-Chao (陈俊超), Li Biao (李彪), Chen Yong (陈勇). Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation[J]. Chin. Phys. B, 2013, 22(11): 110306-110306.

参考文献 52

[1]	Hasegawa A 1989 Optical Solitons in Fibers (Berlin: Springer)
[2]	Pethick C J and Smith H 2002 Bose-Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press)
[3]	Pitaevski L P and Stringari S 2003 Bose-Einstein Condensation (London: Oxford University Press)
[4]	Davydov A S 1991 Solitons in Molecular Systems (Dordrecht: Kluwer Academic)
[5]	Sulem C and Sulem P 2000 The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse (Berlin: Springer)
[6]	Vázquez L, Streit L and Pérez-García V M (eds) 1997 Nonlinear Klein-Gordon and Schrödinger Systems: Theory and Applications (Singapore: World Scientific)
[7]	Kevrekidis P G, Frantzeskakis D J and Carretero-González R 2008 Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment (New York: Springer)
[8]	Mollenauer L F and Gordon J P 2006 Solitons in Optical Fibers (Boston: Academic Press)
[9]	Serkin V N, Hasegawa A and Belyaeva T L 2007 2007 Phys. Rev. Lett. 98 074102
[10]	Khawaja U A 2010 J. Math. Phys. 51 053506
[11]	Liang J W, Xu T, Tang M Y and Liu X D 2013 Nonlinear Analysis: RWA 14 329
[12]	Zhao L C and He S L 2011 Phys. Lett. A 375 3017
[13]	Kumar V R, Radha R and Wadati M 2010 Phys. Lett. A 374 3685
[14]	Radha R and Vinayagam P S 2012 Phys. Lett. A 376 944
[15]	Schumayer D and Apagyi B 2001 J. Phys. A: Math. Gen. 34 4969
[16]	Zhao D, Luo H G and Chai H Y 2008 Phys. Lett. A 372 5644
[17]	Ding C Y, Zhao D and Luo H G 2012 J. Phys. A: Math. Theor. 45 115203
[18]	He X G, Zhao D, Li L and Luo H G 2009 Phys. Rev. E 79 056610
[19]	Kundu A 2009 Phys. Rev. E 79 015601(R)
[20]	Kruglov V I, Peacock A C and Harvey J D 2003 Phys. Rev. Lett. 90 3902
[21]	Pérez-García V M, Torresb P J and Konotop V V 2006 Physica D 221 31
[22]	Belmonte-Beitia J, Pérez-García V M, Vekslerchik V and Konotop V V 2008 Phys. Rev. Lett. 100 164102
[23]	Belmonte-Beitia J and Cuevas J 2009 J. Phys. A: Math. Theor. 42 165201
[24]	Cardoso W B, Avelar A T, Bazeia D and Hussein M S 2010 Phys. Lett. A 374 2356
[25]	Yan Y Z and Konotop V V 2009 Phys. Rev. E 80 036607
[26]	Yan Y Z and Hang C 2009 Phys. Rev. A 80 063626
[27]	Yan Y Z and Jiang D M 2012 Phys. Rev. E 85 056608
[28]	Zhang X F, Hu X H, Liu X X and Liu W M 2009 Phys. Rev. A 79 033630
[29]	Wang D S, Hu X H and Liu W M 2010 Phys. Rev. A 82 023612
[30]	Cardoso W B, Avelar A T and Bazeia D 2012 Phys. Rev. E 86 027601
[31]	Chen J C and Li B 2012 Z. Naturforsch. 67a 483
[32]	Hu X and Li B 2011 Chin. Phys. B 20 050315
[33]	Chen J C, Zhang X F, Li B and Chen Y 2012 Chin. Phys. Lett. 29 070303
[34]	Xiong N and Li B 2012 Chin. Phys. Lett. 29 090303
[35]	Belmonte-Beitia J, Pérez-García V M and Vekslerchik V 2007 Phys. Rev. Lett. 98 064102
[36]	Tang X Y and Shukla P K 2007 Phys. Rev. A 76 013612
[37]	Belmonte-Beitia J, Pérez-García V M and Vekslerchik V 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 158
[38]	Jing J C and Li B 2013 Chin. Phys. B 22 010303
[39]	Song W W, Li Q Y, Li Z D and Fu G S 2010 Chin. Phys. B 19 070503
[40]	Wang H and Li B 2011 Chin. Phys. B 20 040203
[41]	Li B 2007 Int. J. Mod. Phys. C 18 1187
[42]	Chen J C and Li B 2011 Z. Naturforsch. 66a 728
[43]	Chen Y, Li B and Zheng Y 2007 Commun. Theor. Phys. 47 143
[44]	Li B and Chen Y 2007 Chaos Soliton. Fract. 33 532
[45]	Zhong W P and Belić M 2010 Phys, Rev. E 82 047601
[46]	Ding C Y, Zhang X F, Zhao D, Luo H G and Liu W M 2011 Phys. Rev. A 84 053631
[47]	Li B, Zhang X F, Li Y Q, Chen Y and Liu W M 2008 Phys. Rev. A 78 023608
[48]	Brazhnyi V A and Pérez-García V M 2011 Chaos Soliton. Fract. 44 381
[49]	Xuan H N and Zuo M 2011 Commun. Theor. Phys. 56 1035
[50]	Wang Q, Wen L and Li Z D 2012 Chin. Phys. B 21 080501
[51]	Hioe F T 1999 Phys. Rev. Lett. 82 1152
[52]	Hioe F T 2003 J. Phys. A: Math. Gen. 36 7307

Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation

Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 52

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	柴若霖, 谢琼涛, 刘小良. Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials[J]. 中国物理B, 2020, 29(9): 90301-090301.
[2]	杨毅, 蔡绍洪, 隆正文, 陈浩, 龙超云. Exact solution of the (1+2)-dimensional generalized Kemmer oscillator in the cosmic string background with the magnetic field[J]. 中国物理B, 2020, 29(7): 70302-070302.
[3]	董晓菲, 谢幼飞, 陈庆虎. Unified approach to various quantum Rabi models witharbitrary parameters[J]. 中国物理B, 2020, 29(2): 20302-020302.
[4]	Hakan Ciftci, H F Kisoglu. Application of asymptotic iteration method to a deformed well problem[J]. 中国物理B, 2016, 25(3): 30201-030201.
[5]	Ozkan Guner, Ahmet Bekir. Bright and dark soliton solutions for some nonlinear fractional differential equations[J]. 中国物理B, 2016, 25(3): 30203-030203.
[6]	朱维婷, 马松华, 方建平, 马正义, 朱海平. Fusion, fission, and annihilation of complex waves for the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff system[J]. 中国物理B, 2014, 23(6): 60505-060505.
[7]	B. Srividya, L. Kavitha, R. Ravichandran, D. Gopi. Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation[J]. 中国物理B, 2014, 23(1): 10307-010307.
[8]	刘萍, 李子良. Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations[J]. 中国物理B, 2013, 22(5): 50204-050204.
[9]	Vikas Kumar, R. K. Gupta, Ram Jiwari. Comparative study of travelling wave and numerical solutions for the coupled short pulse (CSP) equation[J]. 中国物理B, 2013, 22(5): 50201-050201.
[10]	陈元明, 马松华, 马正义. New exact solutions of (3+1)-dimensional Jimbo-Miwa system[J]. 中国物理B, 2013, 22(5): 50510-050510.
[11]	张聪, 郭文安, 冯世平, 杨师杰. Skyrmion crystals in pseudo-spin-1/2 Bose–Einstein condensates[J]. 中国物理B, 2013, 22(11): 110308-110308.
[12]	Lakhveer Kaur, R. K. Gupta. On certain new exact solutions of the Einstein equations for axisymmetric rotating fields[J]. 中国物理B, 2013, 22(10): 100203-100203.
[13]	Nisha Goyal, R. K. Gupta. New exact solutions of Einstein–Maxwell equations for magnetostatic fields[J]. 中国物理B, 2012, 21(9): 90401-090401.
[14]	杨征, 马松华, 方建平. Soliton excitations and chaotic patterns for the (2+1)-dimensional Boiti–Leon–Pempinelli system[J]. 中国物理B, 2011, 20(6): 60506-060506.
[15]	套格图桑, 那仁满都拉. Constructing infinite sequence exact solutions of nonlinear evolution equations[J]. 中国物理B, 2011, 20(11): 110203-110203.