Domain walls in fractional media

Kumar, Shatrughna; Li, Pengfei; Malomed, Boris A.

doi:10.1103/physreve.106.054207

Cited by 12 publications

(3 citation statements)

References 73 publications

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“…Appropriate numerical methods for the work combining the fractional derivatives, represented by the nonlocal pseudodifferential operators (see Equation 4), and local nonlinearities are available, 24,25 which has made it possible to predict many results for solitons in such systems with the cubic, [26][27][28][29][30][31][32][33][34][35][36][37] cubic-quintic, 38,39 and quadratic 40 nonlinear terms. Other nonlinear states, such as fractional discrete solitons, 41,42 Airy waves, 43 and domain walls, 44 were also predicted in the framework of FNLSEs. Many theoretical results for fractional solitons, in both one-and two-dimensional models, are summarized in recent reviews.…”

Section: Introduction and The Modelmentioning

confidence: 95%

Interactions between fractional solitons in bimodal fiber cavities

Zangmo,

Mayteevarunyoo,

Malomed

2024

Stud Appl Math

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We introduce a system of fractional nonlinear Schrödinger equations (FNLSEs) which model the copropagation of optical waves carried by different wavelengths or mutually orthogonal circular polarizations in fiber‐laser cavities with the effective fractional group‐velocity dispersion (FGVD), which were recently made available to the experiment. In the FNLSE system, the FGVD terms are represented by the Riesz derivative, with the respective Lévy index (LI). The FNLSEs, which include the self‐phase‐modulation (SPM) nonlinearity, are coupled by the cross‐phase‐modulation (XPM) terms, and separated by a group‐velocity (GV) mismatch (rapidity). By means of systematic simulations, we analyze collisions and bound states of solitons in the XPM‐coupled system, varying the LI and GV mismatch. Outcomes of collisions between the solitons include rebound, conversion of the colliding single‐component solitons into a pair of two‐component ones, merger of the solitons into a breather, their mutual passage leading to excitation of intrinsic vibrations, and the elastic interaction. Families of stable two‐component soliton bound states are constructed too, featuring a rapidity which is intermediate between those of the two components.

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Section: Introduction and The Modelmentioning

confidence: 95%

Interactions between fractional solitons in bimodal fiber cavities

Zangmo,

Mayteevarunyoo,

Malomed

2024

Stud Appl Math

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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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“…Moreover, fractional quantum mechanics plays a very crucial role in optical systems [7,[22][23][24][25][26]. In this context, there have been recent theoretical works on domain walls in fractional media [27], fractional diffraction in the context of parity-time symmetric potentials [28][29][30], and on optical solitons [23,, that bought lots of attention. The experimental realization of an optical system representing the fractional Schrödinger equation has been reported very recently in [53].…”

Section: Introductionmentioning

confidence: 99%

One-dimensional Lévy quasicrystal

Chatterjee,

Modak

2023

J. Phys.: Condens. Matter

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Space-fractional quantum mechanics (SFQM) is a generalization of the standard quantum mechanics when the Brownian trajectoriesin Feynman path integrals are replaced by L{'e}vy flights. We introduce L{'e}vy quasicrystal by discretizing the space-fractional Schr$\ddot{\text{o}}$dinger equation using the Gr$\ddot{\text{u}}$nwald-Letnikov derivatives and adding on-site quasiperiodic potential. The discretized version of the usual Schr$\ddot{\text{o}}$dinger equation maps to the Aubry-Andr{'e} Hamiltonian, which supports localization-delocalization transition even in one dimension. We find the similarities between L{'e}vy quasicrystal and the Aubry-Andr{'e} (AA) model with power-law hopping, and show that the L{'e}vy quasicrystal supports a delocalization-localization transition as one tunes the quasiperiodic potential strength and shows the coexistence of localized and delocalized states separated by mobility edge. Hence, a possible realization of SFQM in optical experiments should be a new experimental platform to test the predictions of AA models in the presence of power-law hopping.

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Domain walls in fractional media

Cited by 12 publications

References 73 publications

Interactions between fractional solitons in bimodal fiber cavities

Interactions between fractional solitons in bimodal fiber cavities

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

One-dimensional Lévy quasicrystal

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