On solving cubic-quartic nonlinear Schrödinger equation in a cnoidal trap

Debnath, Argha; Khan, Ayan

doi:10.1140/epjd/e2020-10364-4

Cited by 13 publications

(8 citation statements)

References 30 publications

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“…Here we note that, very recently we have proposed cnoidal solutions of CQNLSE. [ 29 ] There, we have used a cnoidal potential to stabilize the analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Quantum Droplets: An Analytical Approach

Debnath

Khan

2021

Annalen der Physik

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Recent observations of droplets in dipolar and binary Bose–Einstein condensate (BEC) gives motivation to study the theory of droplet formation in detail. Specifically, the authors are interested in investigating the possibility of droplet formation in a quasi‐1D geometry. Recent observations have suggested that droplets are stabilized by competition between effective mean‐field and beyond mean‐field interaction. Hence, it is possible to map the effective equation of motion to a cubic‐quartic nonlinear Schrödinger equation (CQNLSE). Two analytical solutions of the modified Gross–Pitaevskii equation or CQNLSE are obtained and they are verified numerically. Based on their stability, the parameter regime for which droplets can form is investigated. The effective potential allows for conclusions about the regions of soliton domination and self‐bound droplet formations.

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“…Here we note that, very recently we have proposed cnoidal solutions of CQNLSE. [ 29 ] There, we have used a cnoidal potential to stabilize the analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Quantum Droplets: An Analytical Approach

Debnath

Khan

2021

Annalen der Physik

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“…Reference [63] takes the ansatz of the form ψ(z) = A + B cn(z, q) with the external potential as δ(z) = V 0 cn 3 (z, q), where V 0 is the strength of the external potential. The competition between the external potential and the non-linearity allows the system to stabilize.…”

Section: "Cn" Solutionmentioning

confidence: 99%

“…Furthermore, one can observe that it is necessary to impose a condition of β < 0 so that the coherence length remains real. Hence, the cnoidal wave solution reads [63]…”

Section: "Sn" Solutionmentioning

confidence: 99%

“…A kink solution can be observed in a ferromagnet where the different spin domains are separated by the domain walls. In these systems, under the influence of external magnetic fields, the Bloch wall can propagate following the dynamical rules governed by the Sine-Gordon equation, and thus the Bloch walls take the shape of kink [63].…”

Section: Kink-antikink Solutionmentioning

confidence: 99%

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Quantum Droplet in Lower Dimensions

Khan

Debnath

2022

Front. Phys.

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The study of Bose–Einstein condensation (BEC) in lower dimensions plays an important role in understanding the fundamentals of many-body physics as they can be treated theoretically with relative ease and can be verified experimentally. Recently, observation of a liquid-like state in a BEC mixture has been reported along with a theoretical prescription for its observation in the lower dimension. This observation is unique and has serious ramifications in our prevailing conception of the liquid state, which has a deep influence on the van der Waals theory. In explaining the self-bound nature of this state, quantum fluctuation and its fine balance with mean-field (MF) interaction turn out to be playing a key role. Though the experiments are performed predominantly in three dimensions, theoretical studies extend to the lower dimensions. In this brief review, we plan to summarize the recent theoretical advances in droplet research in the lower dimension and elaborate on the description of our contributions. We will mainly focus on analytical results related to this self-bound state in a one-dimension and quasi one-dimension environment. We aim to cover a few results from the family of cnoidal solutions to droplet solutions with smooth transitions between each other, finishing it by carrying a modest discussion on the supersolid phase.

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“…A similar approach was developed for constructing solvable 3D models, which admit factorization of the respective 3D equation into a product of relatively simple 1D equations, which admit exact solutions (in particular, solitons) [73][74][75][76][77]. In fact, the integrability of such specially designed (engineered ) models is not a fundamentally new mathematical finding, because they may be transformed, by means of tricky but explicit transformations of the wave function (or several wave functions, in the case of multi-component systems), spatial coordinates, and the temporal variable, into the classical integrable 1D NLS equation with constant coefficients (or the Manakov's [78] integrable system of the NLS equations) [79,80]. Accordingly, a great variety of integrable and nearly integrable models can be generated by means of inverse engineering, applying generic transformations of the same type to the underlying integrable equation(s) [81].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal engineering of matter-wave solitons in Bose–Einstein condensates

2021

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• A review is focused on 1D, 2D, and 3D matter-wave solitons in Bose-Einstein condensates under the action of spatiotemporally modulated cubic nonlinearity and time-dependent trapping potentials • Most essential problems under the consideration is the shape and stability of solitons and other coherent structures, including stabilization against the critical collapse • Both analytical results (exact and approximate ones) and systematically produced numerical findings are summarized • The modulational instability in these models and its nonlinear development is addressed in detail • Stability and motion of multi-component solitons in binary and spinor (triple) solitons is considered

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On solving cubic-quartic nonlinear Schrödinger equation in a cnoidal trap

Cited by 13 publications

References 30 publications

Investigation of Quantum Droplets: An Analytical Approach

Investigation of Quantum Droplets: An Analytical Approach

Quantum Droplet in Lower Dimensions

Spatiotemporal engineering of matter-wave solitons in Bose–Einstein condensates

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