Discrete Schrodinger equations and dissipative dynamical systems

被引：16

作者：

Abounouh, M. ^{[1
]}

Al Moatassime, H. ^{[1
]}

Chehab, J. P. ^{[2
,3
]}

Dumont, S. ^{[4
]}

Goubet, O. ^{[4
]}

机构：

[1] Univ Cadi Ayyad, Fac Sci & Tech Gueliz, Marrakech, Morocco

[2] Univ Lille 1, Lab Math Paul Painleve, CNRS, UMR 8524, F-59655 Villeneuve Dascq, France

[3] INRIA Futurs, SIMPAF Project, Lille, France

[4] Univ Picardie Jules Verne, CNRS, LAMFA UMR 6140, Amiens, France

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2008年 / 7卷 / 02期

关键词：

finite differences; stability; multilevel decomposition;

D O I：

10.3934/cpaa.2008.7.211

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a Crank-Nicolson scheme to study numerically the long-time behavior of solutions to a one dimensional damped forced nonlinear Schrodinger equation. We prove the existence of a smooth global attractor for these discretized equations. We also provide some numerical evidences of this asymptotical smoothing effect.

引用

页码：211 / 227

页数：17

共 19 条

[1] ON THE DISCRETIZATION OF A PARTIAL-DIFFERENTIAL EQUATION IN THE NEIGHBORHOOD OF A PERIODIC ORBIT [J].

ALOUGES, F ;

DEBUSSCHE, A .

NUMERISCHE MATHEMATIK, 1993, 65 (02) :143-175

[2] ON THE QUALITATIVE BEHAVIOR OF THE ORBITS OF A PARABOLIC PARTIAL-DIFFERENTIAL EQUATION AND ITS DISCRETIZATION IN THE NEIGHBORHOOD OF A HYPERBOLIC FIXED-POINT [J].

ALOUGES, F ;

DEBUSSCHE, A .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1991, 12 (3-4) :253-269

[3]

[Anonymous], APPL ANAL

[4] An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity [J].

Bao, WZ ;

Jaksch, D .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 41 (04) :1406-1426

[5] Nonlinear hybrid procedures and fixed point iterations [J].

Brezinski, C ;

Chehab, JP .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1998, 19 (5-6) :465-487

[6]

CUEVAS J, IN PRESS TRESHOLDS T

[7]

GHIDAGLIA JM, 1988, ANN I H POINCARE-AN, V5, P365

[8]

GOUBET O, 1997, DISCRETE CONT DYN S, V3, P303

[9]

GOUBET O, IN PRESS DISSIPATIVE

[10]

Hale J.K., 1988, MATH SURVEYS MONOGRA, V25

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