On Solving Cubic-Quartic Nonlinear Schrödinger Equation in a Cnoidal Trap
arXiv:2002.04001 · doi:10.1140/epjd/e2020-10364-4
Abstract
The recent observations of quantum droplet in ultra-cold atomic gases have opened up new avenues of fundamental research. The competition between mean-field and beyond mean-field interactions, in ultra-cold dilute alkali gases, are believed to be instrumental in stabilizing the droplets. These new understanding has motivated us to investigate the analytical solutions of a trapped cubic-quartic nonlinear Schrödinger equation (CQNLSE). The quartic contribution in the NLSE is derived from the beyond mean-field formalism of Bose-Einstein condensate (BEC). To the best of our knowledge, a comprehensive analytical description of CQNLSE is non-existent. Here, we study the existence of the analytical solutions which are of the cnoidal type for CQNLSE. The external trapping plays a significant role in the stabilization of the system. In the limiting case, the cnoidal wave solutions lead to the localized solution of bright solution and delocalized kink-antikink pair. The nonexistence of the sinusoidal mode in the current scheme is also revealed in our analysis.
arXiv commentExtensively modified from v1. To appear in Eur. Phys. J. D
References in corpus (21)
- Many-Body Physics with Ultracold Gases
- Theory of Bose-Einstein condensation in trapped gases
- Theory of ultracold Fermi gases
- Formation and Propagation of Matter Wave Soliton Trains
- Formation of a Matter-Wave Bright Soliton
- Quantum liquid droplets in a mixture of Bose-Einstein condensates
- Observation of quantum droplets in a strongly dipolar Bose gas
- Observing the Rosensweig instability of a quantum ferrofluid
- Ultradilute low-dimensional liquids
- Bright soliton to quantum droplet transition in a mixture of Bose-Einstein condensates
- Solitons in combined linear and nonlinear lattice potentials
- A new class of exact solitary wave solutions of one dimensional Gross-Pitaevskii equation
- Heavy Solitons in a Fermionic Superfluid
- Generalized elliptic functions and their application to a nonlinear eigenvalue problem with -Laplacian
- Dilute Fluid Governed by Quantum Fluctuations
- Collective modes across the soliton-droplet crossover in binary Bose mixtures
- Grey solitons in a strongly interacting superfluid Fermi Gas
- Gapped solitons and periodic excitations in strongly coupled BEC
- Bell Soliton in Ultra-cold Atomic Fermi Gas
- Controlled Generation of Nonlinear Resonances through Sinusoidal Lattice Modes in Bose-Einstein Condensate
- Solitons in One Dimensional Systems at BCS-BEC Crossover
Cited by in corpus (8)
- Spatiotemporal engineering of matter-wave solitons in Bose-Einstein condensates
- Investigation of Quantum Droplet: An Analytical Approach
- Dropleton-Soliton Crossover mediated via Trap Modulation
- Josephson dynamics and localization revivals in ultradilute quantum liquids
- Signature of Supersolidity in a Driven Cubic-Quartic Nonlinear Schrödinger Equation
- Dynamics of Bright Soliton Under Cubic-Quartic Interactions in Quasi One-Dimensional Geometry
- Quantum Liquid in Lower Dimensions: From the perspective of Surface Tension
- Collective Excitation of Quantum Droplet with Different Ranges of the Interaction of Pöschl-Teller Potential