Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations

J. M. Ghidaglia

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1989)

  • Volume: 23, Issue: 3, page 433-443
  • ISSN: 0764-583X

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Ghidaglia, J. M.. "Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 23.3 (1989): 433-443. <http://eudml.org/doc/193571>.

@article{Ghidaglia1989,
author = {Ghidaglia, J. M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonlinear Schrödinger equation; finite-dimensional attractor},
language = {eng},
number = {3},
pages = {433-443},
publisher = {Dunod},
title = {Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations},
url = {http://eudml.org/doc/193571},
volume = {23},
year = {1989},
}

TY - JOUR
AU - Ghidaglia, J. M.
TI - Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1989
PB - Dunod
VL - 23
IS - 3
SP - 433
EP - 443
LA - eng
KW - nonlinear Schrödinger equation; finite-dimensional attractor
UR - http://eudml.org/doc/193571
ER -

References

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  3. [3] P. CONSTANTIN, C. FOIAS and R. TEMAM, Attractors representing turbulent flows, Memoirs of A.M.S. 53 (1985) n° 314. Zbl0567.35070MR776345
  4. [4] J. M. GHIDAGLIA, Comportement de dimension finie pour les équations de Schrödinger non linéaires faiblement amorties, C.R. Acad. Sci. Paris, t. 305, Série I (1987) 291-294. Zbl0638.35020MR910362
  5. [5] J. M. GHIDAGLIA, Finite dimensional behavior for weakly damped driven Schrodinger equations, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 5 (1988) 365-405. Zbl0659.35019MR963105
  6. [6] J. M. GHIDAGLIA, Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical System in the long time, J. Diff. Equ. 74 (1988) 369-390. Zbl0668.35084MR952903
  7. [7] J. M. GHIDAGLIA and B. HÉRON, Dimension of the attractors associated to the Ginzburg-Landau partial differential equation, Physica 28D (1987) 282-304. Zbl0623.58049MR914451
  8. [8] J. M. GHIDAGLIA and R. TEMAMAttractors for damped nonlinear hyperbolic equations, J. Math. Pures Appl. 66 (1987) 282-304. Zbl0572.35071MR913856
  9. [9] K. NOZAKI and N. BEKKI, Low-dimensional chaos in a driven damped nonlinear Schrödinger equation, Physica 21D (1986) 381-393. Zbl0607.35017MR862265
  10. [10] N. LEVINSON, Transformation theory of nonlniear differential equations of the second order, Annals of Math. 45 (1944) 723-737. Zbl0061.18910MR11505
  11. V. E. ZAKHAROV and A. B. SHABAT, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics JETP 34 (1972) 62-39. MR406174

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