Analytical spatiotemporal similaritons for the generalized (3 + 1)-dimensional Gross-Pitaevskii equation with an external harmonic trap

Chaos, Solitons and Fractals

Volumn 44, Issue 10, 2011, Pages 862-870

  Dai, Chaoqing ^a,b   Chen, Ruipin ^a   Zhang, Jiefang ^a,c  

^a ZHEJIANG A F UNIVERSITY   (China)

^b SOOCHOW UNIVERSITY   (China)

^c ZHEJIANG UNIVERSITY OF MEDIA AND COMMUNICATIONS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BOSE-EINSTEIN CONDENSATION; HARMONIC ANALYSIS;

GROSS-PITAEVSKII EQUATION; HARMONIC TRAP; SIMILARITON; SIMILARITONS; TIME DEPENDENT;

CONTROL NONLINEARITIES;

EID: 80053007641     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2011.07.004     Document Type: Article

References (40)

1. B.A. Malomed, D. Michalache, F. Wise, and L. Torner Spatiotemporal optical solitons J Opt B 7 2005 R53
2. M. Belić, N. Petrović, W.P. Zhong, R.H. Xie, and G. Chen Analytical light bullet solutions to the generalized (3 + 1)-dimensional nonlinear Schrödinger equation Phys Rev Lett 101 2008 123904
3. C.Q. Dai, Y.Y. Wang, and J.F. Zhang Analytical spatiotemporal localizations for the generalized (3 + 1)-dimensional nonlinear Schrödinger equation Opt Lett 35 2010 1437 1439
4. C.Q. Dai, and J.F. Zhang Exact spatial similaritons and rogons in 2D graded-index waveguides Opt Lett 35 2010 2651 2653
5. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari Theory of Bose-Einstein condensation in trapped gases Rev Mod Phys 71 1999 463 512 (Pubitemid 129330877)
6. V.A. Brazhnyi, and V.M. Pérez-García Stable multidimensional soliton stripes in two-component Bose-Einstein condensates Chaos Solitons Fract 44 2011 381 389
7. J.C. Liang, H.P. Liu, F. Liu, and L. Yi Analytical solutions to the (3 + 1)-dimensional generalized nonlinear Schrödinger equation with varying parameters J Phys A Math Theor 42 2009 335204
8. S.V. Prants Matter-wave chaos with a cold atom in a standing-wave laser field Chaos Solitons Fract 43 2010 1 7
9. N.Z. Petrović, M. Belić, and W.P. Zhong Spatiotemporal wave and soliton solutions to the generalized (3 + 1)-dimensional Gross-Pitaevskii equation Phys Rev E 81 2010 016610
10. S.A. Ponomarenko, and G.P. Agrawal Interactions of chirped and chirp-free similariton in optical fiber amplifiers Opt Exp 15 2007 2963 2973 (Pubitemid 46457159)
11. C.Q. Dai, Y.Y. Wang, and J.F. Zhang Nonlinear similariton tunnelling effect in the birefringent fiber Opt Exp 18 2010 17548 17554
12. C.Q. Dai, Y.Y. Wang, and C.J. Yan Chirped and chirp-free self-similar cnoidal and solitary wave solutions of the cubic-quintic nonlinear Schrödinger equation with distributed coefficients Opt Commun 283 2010 1489 1494
13. C.Q. Dai, Y.Y. Wang, and X.G. Wang Ultrashort self-similar solutions of the cubic-quintic nonlinear Schrödinger equation with distributed coefficients in the inhomogeneous fiber J Phys A Math Theor 44 2011 155203
14. C.Q. Dai, Y.Y. Wang, and J.L. Chen Analytic investigation on the similariton transmission control in the dispersion decreasing fiber Opt Commun 284 2011 3440 3444
15. Y. Ozeki, and T. Inoue Stationary rescaled pulse in dispersion decreasing fiber for pedestal-free pulse compression Opt Lett 31 2006 1606 1608 (Pubitemid 44018038)
16. T.M. Monro, P.D. Millar, L. Poladian, and C.M. de Sterke Self-similar evolution of self-written waveguides Opt Lett 23 1998 268 270 (Pubitemid 128587557)
17. J.D. Moores Nonlinear compression of chirped solitary waves withand without phase modulation Opt Lett 21 1996 555 557 (Pubitemid 126575016)
18. C. Finot, G. Millot, and J.M. Dudley Asymptotic characteristics of parabolic similariton pulses in optical fiber amplifiers Opt Lett 29 2004 2533 2535
19. C. Sulem, and P. Sulem The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse 2000 Springer-Verlag Berlin
20. F.Kh. Abdullaev, J.G. Caputo, R.A. Kraenkel, and B.A. Malomed Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length Phys Rev A 69 2004 063613
21. I. Towers, and B.A. Malomed Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity J Opt Soc Am B 19 2002 537 543
22. L. Wu, L. Li, J.F. Zhang, D. Mihalache, B.A. Malomed, and W.M. Liu Exact solutions of the Gross-Pitaevskii equation for stable vortex modes in two-dimensional Bose-Einstein condensates Phys Rev A 81 2010 061805 R
23. H. Saito, and M. Ueda Dynamically stabilized bright solitons in a two-dimensional Bose-Einstein condensate Phys Rev Lett 90 2003 040403
24. A.C. Newell Nonlinear tunneling J Math Phys 19 1978 1126 1133
25. D. Anderson, M. Lisak, B. Malomed, and M. Quiroga-Teixeiro Tunneling of an optical soliton through a fiber junction J Opt Soc Am B 11 1994 2380 2384
26. V.N. Serkin, V.M. Chapela, J. Percino, and T.L. Belyaeva Nonlinear tunneling of temporal and spatial optical solitons through organic thin films and polymeric waveguides Opt Commun 192 2001 237 244 (Pubitemid 32529106)
27. G. Yang, R. Hao, L. Li, Z. Li, and G. Zhou Cascade compression induced by nonlinear barriers in propagation of optical solitons Opt Commun 260 2006 282 287 (Pubitemid 43326542)
28. W.P. Zhong, and M.R. Belić Soliton tunneling in the nonlinear Schrödinger equation with variable coefficients and an external harmonic potential Phys Rev E 81 2010 056604
29. J. Belmonte-Beitia, V.M. Pérez-García, and V.E. Vekslerchik Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities Phys Rev Lett 98 2007 064102
30. J. Belmonte-Beitia Exact solutions for the quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity Chaos Solitons Fract 41 2009 1005 1009
31. J. Belmonte-Beitia, V.M. Pérez-García, V.E. Vekslerchik, and V.V. Konotop Localized nonlinear waves in systems with time- and space-modulated nonlinearity Phys Rev Lett 100 2008 164102
32. J. Belmonte-Beitia, V.V. Konotop, V.M. Pérez-García, and V.E. Vekslerchik Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: Linear and nonlinear lattices Chaos Solitons Fract 41 2009 1158 1166
33. J. Belmonte-Beitia, and J. Cuevas Solitons for the cubic-quintic nonlinear Schrödinger equation with time- and space-modulated coefficients J Phys A Math Theor 42 2009 165201
34. C.Q. Dai, D.S. Wang, L.L. Wang, J.F. Zhang, and W.M. Liu Quasi-two-dimensional BoseCEinstein condensates with spatially modulated cubicCquintic nonlinearities Ann Phys (NY) 2011 10.1016/j.aop.2011.05.006
35. C.Q. Dai, R.P. Chen, and G.Q. Zhou Spatial solitons with the odd and even symmetries in (2+1)-dimensional spatially inhomogeneous cubic-quintic nonlinear media with transverse W-shaped modulation J Phys B At Mol Opt Phys 44 2011 145401
36. J.F. Zhang, C.Q. Dai, Q. Yang, and J.M. Zhu Variable-coefficient F-expansion method and its application to nonlinear Schrödinger equation Opt Commun 252 2005 408 421 (Pubitemid 41014047)
37. F.D. Zong, C.Q. Dai, Q. Yang, and J.F. Zhang Soliton solutions for variable coefficient nonlinear Schrödinger equation in optical fiber and their application Acta Phys Sin 55 2006 3805 3812 (Pubitemid 44348289)
38. L. Gagnon, and P. Winternitz Symmetry classes of variable coefficient nonlinear Schrödinger equations J Phys A 26 1993 7061 7076
39. V.I. Kruglov, A.C. Peacock, and J.D. Harvey exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients Phys Rev Lett 90 2003 113902
40. L.H. Jiang, and H.Y. Wu Spatiotemporal self-similar waves for the (3 + 1)-dimensional inhomogeneous cubic-quintic nonlinear medium Opt Commun 284 2011 2022 2026