Geodesic
Autoresonance excitation of a~soliton of the nonlinear Schr\"odinger equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 62-66

Voir la notice de l'article provenant de la source Math-Net.Ru

The action of an external parametric perturbation with slowly changing frequency on a soliton of the nonlinear Schrödinger equation is studied. Equations for the time evolution of the parameters of the perturbed soliton are derived. Conditions for the soliton phase locking are found, which relate the rate of change of the perturbation frequency, its amplitude, the wave number, and the phase to the initial data of the soliton. The cases when the initial amplitude of the soliton is small and when the amplitude of the soliton is of the order of unity are considered.
Keywords: autoresonance, nonlinear Schrödinger equation
Mots-clés : perturbation, soliton. 
@article{TIMM_2012_18_2_a5,
     author = {R. N. Garifullin},
     title = {Autoresonance excitation of a~soliton of the nonlinear {Schr\"odinger} equation},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {62--66},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a5/}
}
TY  - JOUR
AU  - R. N. Garifullin
TI  - Autoresonance excitation of a~soliton of the nonlinear Schr\"odinger equation
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2012
SP  - 62
EP  - 66
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a5/
LA  - ru
ID  - TIMM_2012_18_2_a5
ER  - 
%0 Journal Article
%A R. N. Garifullin
%T Autoresonance excitation of a~soliton of the nonlinear Schr\"odinger equation
%J Trudy Instituta matematiki i mehaniki
%D 2012
%P 62-66
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a5/
%G ru
%F TIMM_2012_18_2_a5
R. N. Garifullin. Autoresonance excitation of a~soliton of the nonlinear Schr\"odinger equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 62-66. http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a5/