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arXiv · 2307.06466

Exact Solutions of Augmented GP Equation: Solitons, Droplets and Supersolid

Subhojit Pal·Aradhya Shukla·Prasanta K. Panigrahi
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Abstract

The augmented nonlinear Schr\"odinger equation (ANLSE), describing BEC, with the Lee-Huang-Yang (LHY) correction has exhibited a quantum droplet state, which has found experimental verification. In addition to the droplet, exact kink-antikink and supersolid phases have been recently obtained in different parameter domains. Interestingly, these solutions are associated with a constant background, unlike the form of BEC in quasi-one dimension, where dark, bright, and grey solitons have been experimentally obtained. Here, we connect a wide class of solutions of the ANLSE with the Jacobi elliptic functions using a fractional transformation method in a general scenario. The conserved energy and momentum are obtained in this general setting which differentiates and characterizes the different phases of the solution space. We then concentrate on the Jacobi-elliptic $dn(x, m^2)$ function, as the same is characterized by a non-vanishing background as compared to the other $cn$ and $sn$ functions.

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Subhojit Pal, Aradhya Shukla, Prasanta K. Panigrahi. 2023-07-12. Exact Solutions of Augmented GP Equation: Solitons, Droplets and Supersolid. https://arxiv.org/abs/2307.06466

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