Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations

Agalarov, A. M.; Zhulego, Vladimir; Gadzhimuradov, T. A.

doi:10.1103/physreve.91.042909

Cited by 46 publications

(25 citation statements)

References 34 publications

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“…This is to be contrasted with the familiar multi-component (vector) U (m, n) nonlinear Schrödinger equation [7,10]:…”

Section: Nonlinear Schrödinger Equation and Two-component Chiral Solimentioning

confidence: 99%

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Edge States and Chiral Solitons in Topological Hall and Chern–Simons Fields

Agalarov¹,

Gadzhimuradov²,

Potapov³

et al. 2018

Model. anal. inf. sist.

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The multi-component extension problem of the (2 + 1)D-gauge topological Jackiw-Pi model describing the nonlinear quantum dynamics of charged particles in multi-layer Hall systems is considered. By applying the dimensional reduction (2 + 1)D → (1 + 1)D to Lagrangians with the Chern-Simons topologic fields , multi-component nonlinear Schrodinger equations for particles are constructed with allowance for their interaction. With Hirota's method, an exact two-soliton solution is obtained, which is of interest in quantum information transmission systems due to the stability of their propagation. An asymptotic analysis t → ±∞ of soliton-soliton interactions shows that there is no backscattering processes. We identify these solutions with the edge (topological protected) stateschiral solitons-in the multi-layer quantum Hall systems. By applying the Hirota bilinear operator algebra and a current theorem, it is shown that, in contrast to the usual vector solitons, the dynamics of new solutions (chiral vector solitons) has exclusively unidirectional motion. The article is published in the author's wording.

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“…This is to be contrasted with the familiar multi-component (vector) U (m, n) nonlinear Schrödinger equation [7,10]:…”

Section: Nonlinear Schrödinger Equation and Two-component Chiral Solimentioning

confidence: 99%

“…and a = a * (*-complex conjugation). The parameters k j related to the amplitudes, width and velocity of the j-th soliton [7,10].…”

Section: Nonlinear Schrödinger Equation and Two-component Chiral Solimentioning

confidence: 99%

Edge States and Chiral Solitons in Topological Hall and Chern–Simons Fields

Agalarov¹,

Gadzhimuradov²,

Potapov³

et al. 2018

Model. anal. inf. sist.

View full text Add to dashboard Cite

show abstract

“…Exact solutions.-For the nonlocal system (7) with ǫ x = −1, we will study it some solutions. We make the transformation [24] q 1 (x, t) = p 1 (x, t) + M 12 p 2 (x, t), q 2 (x, t) = −M 11 p 2 (x, t) (25) such that system (7) with ǫ x = −1 reduces to…”

Section: Multi-linear Form and Symmetry Reductionsmentioning

confidence: 99%

Nonlocal general vector nonlinear Schrödinger equations: Integrability, PT symmetribility, and solutions

Yan

2016

Applied Mathematics Letters

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A family of new one-parameter (ǫx = ±1) nonlinear wave models (called G (nm) ǫx model) is presented, including both the local (ǫx = 1) and new integrable nonlocal (ǫx = −1) general vector nonlinear Schrödinger (VNLS) equations with the self-phase, cross-phase, and multi-wave mixing modulations. The nonlocal G (nm) −1 model is shown to possess the Lax pair and infinite number of conservation laws for m = 1. We also establish a connection between the G (nm) ǫx model and some known models. Some symmetric reductions and exact solutions (e.g., bright, dark, and mixed brightdark solitons) of the representative nonlocal systems are also found. Moreover, we find that the new general two-parameter (ǫx, ǫt) model (called G (nm) ǫx,ǫt model) including the G (nm) ǫx model is invariant under the PT -symmetric transformation and the PT symmetribility of its self-induced potentials is discussed for the distinct two parameters (ǫx, ǫt) = (±1, ±1).

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“…Contrast to the single-component equation, the multi-component ones own the intercomponent and inner-component nonlinearity terms [3,23]. Owing to the different polarization of each component may has, vector soliton solutions for the multi-component equations have been displayed in the bright-bright, bright-dark and dark-dark forms [24][25][26][27][28]. Vector solitons have shown to be applicable in the optical switch and logic gate [3,29], since multiple kinds of interactions between the bright vector solitons have been experimentally and theoretically performed, including the shape-changing and shape-preserving interactions [24,25].…”

Section: Introductionmentioning

confidence: 99%

Bright–dark vector soliton solutions for the coupled complex short pulse equations in nonlinear optics

Guo

Wang

2016

Wave Motion

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Under investigation in this paper are the coupled complex short pulse equations, which describe the propagation of ultra-short optical pulses in cubic nonlinear media. Through the Hirota method, bright-dark one-and two-soliton solutions are obtained. Interactions between two bright or two dark solitons are verified to be elastic through the asymptotic analysis. With different parameter conditions of the vector bright-dark two solitons, the oblique interactions, bound states of solitons and parallel solitons are analyzed.

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Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations

Cited by 46 publications

References 34 publications

Edge States and Chiral Solitons in Topological Hall and Chern–Simons Fields

Edge States and Chiral Solitons in Topological Hall and Chern–Simons Fields

Nonlocal general vector nonlinear Schrödinger equations: Integrability, PT symmetribility, and solutions

Bright–dark vector soliton solutions for the coupled complex short pulse equations in nonlinear optics

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