Solitonic model of the condensate

Gelash, Andrey; Agafontsev, Dmitry; Suret, Pierre; Randoux, Stephane

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1103/PhysRevE.104.044213

Title :

Solitonic model of the condensate

Author(s) :

Gelash, Andrey [Auteur]
Institute of Automation and Electrometry of the Siberian Branch of the RAS [IA&E]
Skolkovo Institute of Science and Technology [Moscow] [Skoltech]
Agafontsev, Dmitry [Auteur]
Centre de Mathématiques et de Leurs Applications [CMLA]
Suret, Pierre [Auteur]

Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Randoux, Stephane [Auteur]

Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]

Journal title :

Physical Review E

Publication date :

2021

HAL domain(s) :

Science non linéaire [physics]

English abstract : [en]

We consider a spatially extended box-shaped wave field that consists of a plane wave (the condensate) in the middle and equals zero at the edges, in the framework of the focusing one-dimensional nonlinear Schrodinger ...
Show more >We consider a spatially extended box-shaped wave field that consists of a plane wave (the condensate) in the middle and equals zero at the edges, in the framework of the focusing one-dimensional nonlinear Schrodinger equation. Within the inverse scattering transform theory, the scattering data for this wave field is presented by the continuous spectrum of the nonlinear radiation and the soliton eigenvalues together with their norming constants; the number of solitons N is proportional to the box width. We remove the continuous spectrum from the scattering data and find analytically the specific corrections to the soliton norming constants that arise due to the removal procedure. The corrected soliton parameters correspond to symmetric in space N-soliton solution, as we demonstrate analytically in the paper. Generating this solution numerically for N up to 1024, we observe that, at large N, it converges asymptotically to the condensate, representing its solitonic model. Our methods can be generalized for other strongly nonlinear wave fields, as we demonstrate for the hyperbolic secant potential, building its solitonic model as well.Show less >

Language :

Anglais

ANR Project :

Fibres optiques pour les hauts Flux
Centre Européen pour les Mathématiques, la Physique et leurs Interactions
ULNE

Collections :

Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM) - UMR 8523

Source :

Harvested from HAL

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