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Applicable Analysis
An International Journal
Volume 57, 1995 - Issue 1-2
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Original Articles

White noise in the two-dimensional nonlinear schrödinger equation

O. Bang Laboratory of Applied Mathematical Physics, Technical University of Denmark, Denmark, DK-2800
,
P.L. Christiansen Laboratory of Applied Mathematical Physics, Technical University of Denmark, Denmark, DK-2800
,
F. If2 Laboratory of Applied Mathematical Physics, Technical University of Denmark, Denmark, DK-2800View further author information
,
K.⊘. Rasmussen Laboratory of Applied Mathematical Physics, Technical University of Denmark, Denmark, DK-2800View further author information
&
Y.B. Gaididei Institute for Theoretical Physics, UkraineView further author information
Pages 3-15 | Received 23 Apr 1994, Published online: 02 May 2007

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Jiarui Liang, Tianlong Shen, Xu Qian & Songhe Song. (2019) Time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by Gaussian white noise. Stochastic Analysis and Applications 37:2, pages 123-136.
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Marc Barton-Smith. (2004) Global Solution for a Stochastic Ginzburg-Landau Equation with Multiplicative Noise. Stochastic Analysis and Applications 22:1, pages 1-18.
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A. de Bouard & A. Debussche. (2003) The Stochastic Nonlinear Schrödinger Equation in H 1 . Stochastic Analysis and Applications 21:1, pages 97-126.
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M. Mirzazadeh, M. Eslami & Anjan Biswas. (2014) Dispersive optical solitons by Kudryashov's method. Optik 125:23, pages 6874-6880.
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M. Eslami, M. Mirzazadeh, B. Fathi Vajargah & Anjan Biswas. (2014) Optical solitons for the resonant nonlinear Schrödinger's equation with time-dependent coefficients by the first integral method. Optik 125:13, pages 3107-3116.
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A.A.M. Arafa & S.Z. Rida. (2012) Numerical solutions for some generalized coupled nonlinear evolution equations. Mathematical and Computer Modelling 56:11-12, pages 268-277.
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Arnaud Debussche & Yoshio Tsutsumi. (2011) 1D quintic nonlinear Schrödinger equation with white noise dispersion. Journal de Mathématiques Pures et Appliquées 96:4, pages 363-376.
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L. Kavitha, N. Akila, A. Prabhu, O. Kuzmanovska-Barandovska & D. Gopi. (2011) Exact solitary solutions of an inhomogeneous modified nonlinear Schrödinger equation with competing nonlinearities. Mathematical and Computer Modelling 53:5-6, pages 1095-1110.
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Eric Gautier. (2005) Uniform large deviations for the nonlinear Schrödinger equation with multiplicative noise. Stochastic Processes and their Applications 115:12, pages 1904-1927.
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Arnaud Debussche & Anne de Bouard. (2005) Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise. The Annals of Probability 33:3.
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Anjan Biswas. (2005) Stochastic perturbation of dispersion-managed optical solitons. Optical and Quantum Electronics 37:7, pages 649-659.
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Anjan Biswas. (2004) Stochastic perturbation of optical solitons in Schrödinger–Hirota equation. Optics Communications 239:4-6, pages 461-466.
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G P Flessas, P G L Leach & A N Yannacopoulos. (2004) Stochastic effects on the nonlinear Schrödinger equation. Journal of Optics B: Quantum and Semiclassical Optics 6:5, pages S161-S168.
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D. I. Zhukhovitskii, W. F. Schmidt & E. Illenberger. (2003) Stability of negative ions near the surface of a solid. Journal of Experimental and Theoretical Physics 97:3, pages 606-614.
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E A Saied, Reda G Abd El-Rahman & Marwa I Ghonamy. (2003) On the exact solution of (2 1)-dimensional cubic nonlinear Schr dinger (NLS) equation. Journal of Physics A: Mathematical and General 36:24, pages 6751-6770.
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Ole Bang, Wieslaw Krolikowski, John Wyller & Jens Juul Rasmussen. (2002) Collapse arrest and soliton stabilization in nonlocal nonlinear media. Physical Review E 66:4.
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Till Kamppeter, Franz G. Mertens, Esteban Moro, Angel Sánchez & A. R. Bishop. (1999) Stochastic vortex dynamics in two-dimensional easy-plane ferromagnets: Multiplicative versus additive noise. Physical Review B 59:17, pages 11349-11357.
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F.Kh. Abdullaev, A.A. Abdumalikov & B.B. Baizakov. (1997) Propagation of chirped optical solitons in fibers with randomly varying parameters. Optics Communications 138:1-3, pages 49-54.
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Peter L. Christiansen, Yuri B. Gaididei, Magnus Johansson & Kim Ø. Rasmussen. (1997) Breatherlike excitations in discrete lattices with noise and nonlinear damping. Physical Review B 55:9, pages 5759-5766.
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Peter L. Christiansen, Yuri B. Gaididei, Magnus Johansson, Kim Ø. Rasmussen & Irina I. Yakimenko. (1996) Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise. Physical Review E 54:1, pages 924-930.
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K.Ø. Rasmussen, Yu.B. Gaididei, O. Bang & P.L. Christiansen. (1996) Nonlinear and stochastic modelling of energy transfer in Scheibe aggregates. Mathematics and Computers in Simulation 40:3-4, pages 339-358.
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Yu B Gaididei, S F Mingaleev, I I Yakimenko, P L Christiansen, M Johansson & K Ø Rasmussen. (1996) The nonlinear Schrödinger system: collapse, nonlinear damping, noise, impurities and nonlocal dispersion. Physica Scripta T67, pages 151-159.
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P.L. Christiansen, K.Ø. Rasmussen, O. Bang & Yu.B. Gaididei. (1995) The temperature-dependent collapse regime in a nonlinear dynamical model of Scheibe aggregates. Physica D: Nonlinear Phenomena 87:1-4, pages 321-324.
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Yu. B. Gaididei, K. Ø. Rasmussen & P. L. Christiansen. (1995) Nonlinear excitations in two-dimensional molecular structures with impurities. Physical Review E 52:3, pages 2951-2962.
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