Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations
ESAIM: Modélisation mathématique et analyse numérique, Tome 23 (1989) no. 3, pp. 433-443.
@article{M2AN_1989__23_3_433_0,
     author = {Ghidaglia, J. M.},
     title = {Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic {Schr\"odinger} equations},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {433--443},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {23},
     number = {3},
     year = {1989},
     mrnumber = {1014484},
     zbl = {0688.35084},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1989__23_3_433_0/}
}
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: Modélisation mathématique et analyse numérique
PY  - 1989
SP  - 433
EP  - 443
VL  - 23
IS  - 3
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1989__23_3_433_0/
LA  - en
ID  - M2AN_1989__23_3_433_0
ER  - 
%0 Journal Article
%A Ghidaglia, J. M.
%T Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1989
%P 433-443
%V 23
%N 3
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1989__23_3_433_0/
%G en
%F M2AN_1989__23_3_433_0
Ghidaglia, J. M. Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 23 (1989) no. 3, pp. 433-443. http://archive.numdam.org/item/M2AN_1989__23_3_433_0/

[1] J. E. Billoti and J. P. La Salle, Dissipative periodic processes, Bull. Amer. Math. Soc. 77 (1971) 1082-1088. | MR | Zbl

[2] K. J. Blow and N. J. Doran, Global and local chaos in the pumped nonlinear Schrödinger equation, Physical Review Letters 52 (1984) 526-539.

[3] P. Constantin, C. Foias and R. Temam , Attractors representing turbulent flows, Memoirs of A.M.S. 53 (1985) n° 314. | MR | Zbl

[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. | MR | Zbl

[5] J. M. Ghidaglia, Finite dimensional behavior for weakly damped driven Schrodinger equations, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 5 (1988) 365-405. | Numdam | MR | Zbl

[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. | MR | Zbl

[7] J. M. Ghidaglia and B. Héron, Dimension of the attractors associated to the Ginzburg-Landau partial differential equation, Physica 28D (1987) 282-304. | MR | Zbl

[8] J. M. Ghidaglia and R. Temam Attractors for damped nonlinear hyperbolic equations, J. Math. Pures Appl. 66 (1987) 282-304. | MR

[9] K. Nozaki and N. Bekki, Low-dimensional chaos in a driven damped nonlinear Schrödinger equation, Physica 21D (1986) 381-393. | MR | Zbl

[10] N. Levinson , Transformation theory of nonlniear differential equations of the second order, Annals of Math. 45 (1944) 723-737. | MR | Zbl

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. | MR