Chinese Journal of Quantum Electronics, Volume. 26, Issue 4, 465(2009)
Exact self-similar solution to a generalized nonlocal nonlinear Schr dinger model
[1] [1] Barenblatt G I. Scaling, Self-similarity, and Intermediate Asymptotics [M]. Cambridge: Cambridge University Press, 1996.
[2] [2] Olver P J. Applications of Lie Groups to Differential Equations [M]. New York: Springer, 1986.
[3] [3] Turitsyn S K. Breathing self-similar dynamics and oscillatory tails of the chirped dispersion-managed soliton [J]. Phys. Rev. E, 1998, 58: R1256.
[4] [4] Kruglov V I, Peacock A C, Harvey J D. Exact self-similar solutions of the generalized nonlinear Schr dinger equation with distributed coefficients [J]. Phys. Rev. Lett., 2003, 90: 113902.
[5] [5] Chen S, Yi L, Guo D, et al. Self-similar evolutions of parabolic, HG, and hybrid optical pulses: universality and diversity [J]. Phys. Rev. E, 2005, 72: 016622.
[6] [6] Chen S, Yi L. Chirped self-similar solutions of a generalized nonlinear Schr dinger equation model [J]. Phys. Rev. E, 2005, 71: 016606.
[7] [7] Raju T S, Panigrahi P K, Porezian K. Self-similar propagation and compression of chirped self-similar waves in asymmetric twin-core fibers with nonlinear gain [J]. Phys. Rev. E, 2005, 72: 046612.
[8] [8] Wadati M. B cklund transformation for solutions of the modified Korteweg-de Vries equation [J]. J. Phys. Soc. Japan, 1974, 36: 1498.
[9] [9] Ablowitz M J, Clarkson P A. Nonlinear Evolution Equations and Inverse Scattering [M]. Cambridge: Cambridge University Press, 1999.
[12] [12] Zhang Shaowu, Yi Lin. Exact solutions of a generalized nonlinear Schr dinger equation [J]. Phys. Rev. E, 2008, 78: 026602.
[13] [13] Shih M F, Segev M, Salamo G. Three-dimensional spiraling of interacting spatial solitons [J]. Phys. Rev. Lett., 1997, 78: 2551.
[14] [14] Werner A G J, Hensler S, Stuhler J, et al. Bose-Einstein condensation of chromium [J]. Phys. Rev. Lett., 2005, 94: 160401.
[15] [15] Lindl J D. Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain [J]. Phys. Plasmas, 1995, 2(11): 3933.
[16] [16] Korabel N, Klages R. Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems [J]. Phys. Rev. Lett., 2002, 89: 214102.
[17] [17] Fermann M E, Kruglov V I. Thomsen B C, et al. Self-similar propagation and amplification of parabolic pulses in optical fibers [J]. Phys. Rev. Lett., 2000, 84: 6010.
[18] [18] Chang G, Winful H G, Galvanauskas A, et al. Self-similar solutions of the generalized nonlinear Schr dinger equation with distributed coefficients [J]. Phys. Rev. E, 2005, 72: 016609.
[19] [19] Peccianti M, Brzdakiewicz K A, Assanto G. Nonlocal spatial soliton interactions in nematic liquid crystals [J]. Opt. Lett., 2002, 27: 1460.
[20] [20] Królikowski W, Bang O. Solitons in nonlocal nonlinear media: Exact solutions [J]. Phys. Rev. E, 2000, 63: 016610.
[21] [21] Conti C, Peccianti M, Assanto G. Observation of optical spatial solitons in a highly nonlocal medium [J]. Phys. Rev. Lett., 2004, 92: 113902.
[22] [22] Zhong W, Yi L. Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media [J]. Phys. Rev. A, 2007, 75: R061801.
[23] [23] Mihalache D, Mazilu D, Lederer F, et al. Stable solitons of even and odd parities supported by competing nonlocal nonlinearities [J]. Phys. Rev. E, 2006, 74: 066614.
[24] [24] Królikowski W, Bang O, Rasmussen J J, et al. Modulational instability in nonlocal nonlinear Kerr media [J]. Phys. Rev. E, 2001, 64: 016612.
[25] [25] Agrawal G P. Nonlinear Fiber Optics [M]. 4th ed., Boston: Academic Press, 2006. Chap.2.
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ZHANG Shao-wu, YI Lin. Exact self-similar solution to a generalized nonlocal nonlinear Schr dinger model[J]. Chinese Journal of Quantum Electronics, 2009, 26(4): 465
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Received: Sep. 4, 2008
Accepted: --
Published Online: May. 24, 2010
The Author Email: Shao-wu ZHANG (zsw2622@vip.163.com)
CSTR:32186.14.