An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System

In this work, we introduce and theoretically analyze various computational techniques to approximate the solutions of solve a fractional extension of a double condensate system. More precisely, the continuous model extends the well-known Gross-Pitaevskii equation to the fractional scenario, and considering two interacting condensates. The mathematical system considers two complex-valued regimes with coupling, and a mass and energy functions are associated to this model. Both are constant in time. Here, various discretizations are analyzed CMMSE: analysis and comparison of some numerical methods to solve this system. Some of them are able to preserve the mass and the energy, some are not. We discuss the existence of solutions, the consistency of the models, the stability and the convergence. Finally, from the computational point of view, some algorithms are simpler to code than others. In fact, those for which the mass and the energy are conserved are more difficult to implement. We discuss here pros and cons.

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“…Finally, we introduce our fourth numerical algorithm [10] to approximate the solution of (3) on Ω × [0, T ]:…”

Section: Methodsmentioning

confidence: 99%

CMMSE: analysis and comparison of some numerical methods to solve a nonlinear fractional Gross–Pitaevskii system

et al. 2022

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“…The realization of BEC in atomic gases with almost vanishing interactions recreates the general behavior of nonlinear matter waves [16][17][18][19]. Different analytical developments and laboratory studies have directed their interest on the evolution and non destructive process in the two component BEC dark solitons and its nonlinear excited levels in specific trapping of magnetic type that have been modeled by the Gross-Pitaevskii model [38][39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Analytical soliton solutions for the beta fractional derivative Gross–Pitaevskii system with linear magnetic and time dependent laser interactions

Yépez-Martínez,

Inc,

Alqahtani

2024

Phys. Scr.

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The local conformable beta Atangana derivative will be considered for the introductionof the fractional Gross-Pitaevskii model with conformable derivatives of beta type. Solitonsanalytical expressions are constructed by sub-equation method with elliptical functions.New entire family of solitons were determined by considering the arising constrains over theparameters of the nonlinear fractional Gross-Pitaevskii system. The analytical expressionsfor the solitons in the fractional order case reduce to the well known solitons previouslyreported for hyperbolic and periodic tan-type singular solutions for the integer order limitvalue, when special cases of the Jacobi elliptic functions are considered. Solitons propertiesare depicted in 3-D, level and 2-D illustrations. The fractional solitons here introducedposses some interesting time evolution behavior observed in the 3-D representations, thesetime properties are not present in the integer order case and has an important dependencyon the fractional parameter of the beta derivative. The solitons here introduced for thenonlinear fractional Gross-Pitaevskii equation will be very useful in future works where additional interactions will be introduced for the study of different Bose-Einstein condensation phenomena or other nonlinear phenomena where non regular oscillations will be involved.

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Ultrashort optical pulses with nonlinear chirps in non-Kerr media exhibiting higher-order nonlinearities

Kengne

2023

Opt Quant Electron

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An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional Two-Component Gross–Pitaevskii-Type System

Cited by 4 publications

References 30 publications

CMMSE: analysis and comparison of some numerical methods to solve a nonlinear fractional Gross–Pitaevskii system

CMMSE: analysis and comparison of some numerical methods to solve a nonlinear fractional Gross–Pitaevskii system

Analytical soliton solutions for the beta fractional derivative Gross–Pitaevskii system with linear magnetic and time dependent laser interactions

Ultrashort optical pulses with nonlinear chirps in non-Kerr media exhibiting higher-order nonlinearities

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