Stability of (1 + 1)-dimensional coupled nonlinear Schrödinger equation with elliptic potentials

Nath, Debraj; Saha, Naresh; Roy, Barnana

doi:10.1140/epjp/i2018-12308-3

Cited by 6 publications

(5 citation statements)

References 40 publications

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“…It is interesting to observe that solution (13) is stable in a connected region I 7 , which entirely lies in PT unbroken and there is no stable PT broken mode. [64,65]. In the second case g = 1, the existence of BS in (w 0 , v 0 ) and (w 0 , β) planes are shown in Fig.…”

Section: B Stability Of Bsmentioning

confidence: 86%

Connected and disconnected stable regions of solitons of nonlinear Schrödinger equation with $\mathcal{PT}$-symmetric potential

Ghosh,

Das,

Nath

2021

Preprint

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We have considered cubic nonlinear Schrödinger equation along with supersymmetric PT like potential and obtained exact stationary solutions in terms of bright and brigh-dark interacting solitons. The PT broken and PT unbroken regions are demonstrated also depicted. Connected and disconnected stable regions of bright and dark solitons are examined incorporating linear stability analysis validated by direct numerical simulations. Moreover, the strength of stability has been illustrated through excitations of bright and dark solitons.

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Section: B Stability Of Bsmentioning

confidence: 86%

Connected and disconnected stable regions of solitons of nonlinear Schrödinger equation with $\mathcal{PT}$-symmetric potential

Ghosh,

Das,

Nath

2021

Preprint

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“…Combining Equations (67) and (68) with expression (65), we can give the solution of Equation (1) which is an elliptic double periodic function solution, where ξ = μðt − 2α Ð x a βðςÞdςÞ.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

“…Remark 4. In this section, we mainly discuss the solution ψðt , xÞ of Equation (1). Similarly, we can easily obtain the solution ϕðt, xÞ of Equation (1) through their relationship Ψ = łΦ.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

“…The coupled nonlinear Schrödinger (CNLS) equations [1][2][3] are a very important mathematical physical model in the fields of quantum mechanics, nonlinear optics, optical fiber communication, Bose-Einstein condensate, fluid mechanics, and so on. Because of its importance, many new methods and techniques have been proposed to study the CNLS equation, which include the Bäcklund transformation, the variational iteration method, the extended unified method, and the Hirota method [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

Zhao

Han

2021

Advances in Mathematical Physics

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In this paper, the dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete discrimination system method. Firstly, coupled nonlinear Schrödinger equations with variable coefficients are transformed into coupled nonlinear ordinary differential equations by the traveling wave transformations. Then, phase portraits of coupled nonlinear Schrödinger equations with variable coefficients are plotted by selecting the suitable parameters. Furthermore, the traveling wave solutions of coupled nonlinear Schrödinger equations with variable coefficients which correspond to phase orbits are easily obtained by applying the method of planar dynamical systems, which can help us to further understand the propagation of the coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optics. Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed.

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“…In BEC applications, these systems have enormous physical interest, since the model describes two hyperfine levels of an atomic BEC. Different papers have studied exact soliton solutions for similar systems in the case of homogeneous nonlinearities [20][21][22][23][24][25]. In [26], the authors report the existence of different analytical solutions as bright-bright, dark-dark and dark-bright solutions of the two-component system with spatially inhomogeneous nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Explicit solutions with non-trivial phase of the inhomogeneous coupled two-component NLS system

Belmonte-Beitia¹,

Güngör²,

Torres³

2019

J. Phys. A: Math. Theor.

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In this article, we construct novel explicit solutions for nonlinear Schrödinger systems with spatially inhomogeneous nonlinearity by means of the Lie symmetry method. We focus the attention to solutions with non-trivial phase, which have been scarcely considered in the related literature. To get started, the theoretical method based on Lie symmetries is exposed, thus reducing the problem to the integrability of an ODE. The non-trivial phase introduces a singular term into the ODE. Then, the method is used to construct new families of analytical solutions. Some illustrative examples are provided.

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Stability of (1 + 1)-dimensional coupled nonlinear Schrödinger equation with elliptic potentials

Cited by 6 publications

References 40 publications

Connected and disconnected stable regions of solitons of nonlinear Schrödinger equation with $\mathcal{PT}$-symmetric potential

Connected and disconnected stable regions of solitons of nonlinear Schrödinger equation with $\mathcal{PT}$-symmetric potential

Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

Explicit solutions with non-trivial phase of the inhomogeneous coupled two-component NLS system

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