Soliton dynamics for trapped Bose-Einstein condensate with higher-order interaction

We study the sonic horizon formation problem for quantum system incorporating septic nonlinearity, which is modeled by the nonlinear Schrödinger equation (NLSE) with nonlinearity up to septic order. Based on the F-expansion method combined with modulus-phase transformation, we derived the soliton solutions of such NLSE for the one-dimensional and three-dimensional scenarios, from which the sonic horizon formation dynamical variables are derived. We identify that the distribution of system flow velocity and sound velocity, which determine the occurrence of the sonic horizon, agree well with the corresponding quantities obtained from pure numerical evaluation, demonstrating the applicability of the theoretical approach adopted in this study.

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

Guo

Cheng

Okacha

et al. 2021

AIP Advances

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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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Soliton dynamics for trapped Bose-Einstein condensate with higher-order interaction

Cited by 10 publications

References 25 publications

Interactions of solitons, dromion-like structures and butterfly-shaped pulses for variable coefficient nonlinear Schrödinger equation

Interactions of solitons, dromion-like structures and butterfly-shaped pulses for variable coefficient nonlinear Schrödinger equation

Sonic horizon dynamics for quantum systems with cubic-quintic-septic nonlinearity

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

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