Two-dimensional solitons in extended GPE models with Lee-Huang-Yang corrections

arXiv:2607.16820v1 Announce Type: cross Abstract: We investigate the existence and dynamics of two-dimensional solitary waves in a quantum droplet environment described by the extended Gross-Pitaevskii equation featuring logarithmic mean-field and Lee-Huang-Yang interactions. In the modulationally stable regime of the background, we employ suitable multiscale asymptotic methods to derive effective nonlinear integrable models corresponding to the Kadomtsev-Petviashvili and Davey-Stewartson equations. Based on these reduced models, we construct approximate analytical solutions describing line solitons, algebraically localized lump solitons, ring solitons, and exponentially localized dromions embedded on the droplet background. The dynamical robustness of these solutions is monitored through numerical simulations. Line, lump and ring solitons stay closest to the theoretical predictions, although progressively deviate due to the emergence of small-amplitude radiation, while dromions depart from their analytical waveform the most, although they roughly maintain their shape. Our results unveil unprecedented multidimensional soliton solutions in models featuring the competition of mean-field and quantum fluctuations and as such are amenable to current ultracold atom experiments.

Abstract:We investigate the existence and dynamics of two-dimensional solitary waves in a quantum droplet environment described by the extended Gross-Pitaevskii equation featuring logarithmic mean-field and Lee-Huang-Yang interactions. In the modulationally stable regime of the background, we employ suitable multiscale asymptotic methods to derive effective nonlinear integrable models corresponding to the Kadomtsev-Petviashvili and Davey-Stewartson equations. Based on these reduced models, we construct approximate analytical solutions describing line solitons, algebraically localized lump solitons, ring solitons, and exponentially localized dromions embedded on the droplet background. The dynamical robustness of these solutions is monitored through numerical simulations. Line, lump and ring solitons stay closest to the theoretical predictions, although progressively deviate due to the emergence of small-amplitude radiation, while dromions depart from their analytical waveform the most, although they roughly maintain their shape. Our results unveil unprecedented multidimensional soliton solutions in models featuring the competition of mean-field and quantum fluctuations and as such are amenable to current ultracold atom experiments.

Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)

arXiv:2607.16820 [cond-mat.quant-gas]

(or arXiv:2607.16820v1 [cond-mat.quant-gas] for this version)

https://doi.org/10.48550/arXiv.2607.16820 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Two-dimensional solitons in extended GPE models with Lee-Huang-Yang corrections

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