Gray and black solitons of nonlocal ...
Document type :
Pré-publication ou Document de travail
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Title :
Gray and black solitons of nonlocal Gross-Pitaevskii equations: existence, monotonicity and nonlocal-to-local limit
Author(s) :
De Laire, André [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
López-Martínez, Salvador [Auteur]
Universidad Autónoma de Madrid [UAM]

Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
López-Martínez, Salvador [Auteur]
Universidad Autónoma de Madrid [UAM]
English keyword(s) :
Gross-Pitaevskii equation
defocusing nonlocal Schrödinger equation
traveling waves
dark solitons
nonlocal optical solitons
nonzero boundary conditions at infinity
defocusing nonlocal Schrödinger equation
traveling waves
dark solitons
nonlocal optical solitons
nonzero boundary conditions at infinity
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
This article investigates the qualitative aspects of dark solitons of one-dimensional Gross-Pitaevskii equations with general nonlocal interactions, which correspond to traveling waves with subsonic speeds. Under general ...
Show more >This article investigates the qualitative aspects of dark solitons of one-dimensional Gross-Pitaevskii equations with general nonlocal interactions, which correspond to traveling waves with subsonic speeds. Under general conditions on the potential interaction term, we provide uniform bounds, demonstrate the existence of symmetric solitons, and identify conditions under which monotonicity is lost. Additionally, we present new properties of black solitons. Moreover, we establish the nonlocal-to-local convergence, i.e. the convergence of the soliton of the nonlocal model toward the explicit dark solitons of the local Gross-Pitaevskii equation.Show less >
Show more >This article investigates the qualitative aspects of dark solitons of one-dimensional Gross-Pitaevskii equations with general nonlocal interactions, which correspond to traveling waves with subsonic speeds. Under general conditions on the potential interaction term, we provide uniform bounds, demonstrate the existence of symmetric solitons, and identify conditions under which monotonicity is lost. Additionally, we present new properties of black solitons. Moreover, we establish the nonlocal-to-local convergence, i.e. the convergence of the soliton of the nonlocal model toward the explicit dark solitons of the local Gross-Pitaevskii equation.Show less >
Language :
Anglais
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Submission date :
2025-01-24T12:48:03Z
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