Soliton evolution and associated sonic horizon formation dynamics in two-dimensional Bose–Einstein condensate with quintic-order nonlinearity

Wang, Ying; Chen, Yujie; Dai, Jun; Zhao, Li; Wen, Wen; Wang, Wei

doi:10.1063/5.0031741

Chaos: An Interdisciplinary Journal of Nonlinear Science

2021

DOI: 10.1063/5.0031741

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Soliton evolution and associated sonic horizon formation dynamics in two-dimensional Bose–Einstein condensate with quintic-order nonlinearity

Ying Wang

Yujie Chen

Jun Dai

et al.

Abstract: This study explored the two-dimensional Bose–Einstein condensate with an inter-particle nonlinear interaction up to quintic order. Based on the two-dimensional Gross–Pitaevskii equation model with quintic-order nonlinearity, we first derived the bright soliton solution for the system based on the self-similar approach and the modified variational method. We identified that the kinematic quantities derived from the two methods agreed very well. The two-dimensional sonic horizon formation dynamics was then calcu… Show more

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Cited by 5 publications

References 29 publications

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Solitons for a generalized reaction–diffusion equation with the higher‐order power‐law nonlinearity in (1+1)‐ and (2+1)‐dimensional systems

Tang,

Wang,

Bao

et al. 2024

Math Methods in App Sciences

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For the systems modeled by a generalized reaction–diffusion equation with the higher‐order quintic nonlinearity, we explore the soliton dynamics via the F‐expansion method. By the novel F‐base function ansatz, we first derived the bright soliton and kink soliton solutions for the one‐dimensional case of the reaction–diffusion equation with quintic nonlinearity. Furthermore, we employed self‐similar techniques to analyze the higher‐dimensional dynamics of bright soliton and kink soliton solutions supported by the (2+1)‐dimensional reaction–diffusion equation system with quintic nonlinearity. Additionally, we conducted stability analysis of derived soliton solutions. Our theoretical results demonstrate that under certain parametric setting, the reaction–diffusion equation model with higher‐order nonlinearity supports bright soliton and kink soliton in higher‐dimensional as well as lower dimensional setting, which provides guidance for observing and investigating soliton behavior in systems modeled by the reaction–diffusion equation with higher‐order quintic nonlinearity.

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Solitons for a generalized reaction–diffusion equation with the higher‐order power‐law nonlinearity in (1+1)‐ and (2+1)‐dimensional systems

Tang,

Wang,

Bao

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Bright soliton dynamics for seventh degree nonlinear systems with higher-order dispersion

et al. 2021

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In this study, we investigate the typical systems modeled by the (3 + 1)-dimensional as well as (1 + 1)-dimensional Schrödinger equations incorporating third-order dispersion effects, higher-order scattering effects, and cubic–fifth–seventh degree nonlinear interactions. We use the F-expansion method and the self-similar method to solve the higher-order Schrödinger equation for one-dimensional and three-dimensional settings, respectively, identifying typical bright soliton solutions under appropriate system settings. The bright soliton features are demonstrated analytically in regions around the soliton peak region. Pictorial bright soliton features are demonstrated for the three-dimensional setting as well as one-dimensional setting. Our work shows the applicability of the theoretical treatment utilized in studying bright soliton dynamics for systems with third-order dispersion and seventh degree nonlinearity.

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Controllable nonautonomous localized waves and dynamics for a quasi-1D Gross–Pitaevskii equation in Bose–Einstein condensations with attractive interaction

Wang,

Yang,

Tian

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper investigates dynamical behaviors and controllability of some nonautonomous localized waves based on the Gross–Pitaevskii equation with attractive interatomic interactions. Our approach is a relation constructed between the Gross–Pitaevskii equation and the standard nonlinear Schrödinger equation through a new self-similarity transformation which is to convert the exact solutions of the latter to the former’s. Subsequently, one can obtain the nonautonomous breather solutions and higher-order rogue wave solutions of the Gross–Pitaevskii equation. It has been shown that the nonautonomous localized waves can be controlled by the parameters within the self-similarity transformation, rather than relying solely on the nonlinear intensity, spectral parameters, and external potential. The control mechanism can induce an unusual number of loosely bound higher-order rogue waves. The asymptotic analysis of unusual loosely bound rogue waves shows that their essence is energy transfer among rogue waves. Numerical simulations test the dynamical stability of obtained localized wave solutions, which indicate that modifying the parameters in the self-similarity transformation can improve the stability of unstable localized waves and prolong their lifespan. We numerically confirm that the rogue wave controlled by the self-similarity transformation can be reproduced from a chaotic initial background field, hence anticipating the feasibility of its experimental observation, and propose an experimental method for observing these phenomena in Bose–Einstein condensates. The method presented in this paper can help to induce and observe new stable localized waves in some physical systems.

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Soliton evolution and associated sonic horizon formation dynamics in two-dimensional Bose–Einstein condensate with quintic-order nonlinearity

Cited by 5 publications

References 29 publications

Solitons for a generalized reaction–diffusion equation with the higher‐order power‐law nonlinearity in (1+1)‐ and (2+1)‐dimensional systems

Solitons for a generalized reaction–diffusion equation with the higher‐order power‐law nonlinearity in (1+1)‐ and (2+1)‐dimensional systems

Bright soliton dynamics for seventh degree nonlinear systems with higher-order dispersion

Controllable nonautonomous localized waves and dynamics for a quasi-1D Gross–Pitaevskii equation in Bose–Einstein condensations with attractive interaction

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