Vector bright solitons and their interactions of the couple Fokas–Lenells system in a birefringent optical fiber

Zhang, Chen-Rong; Tian, Bo; Qu, Qi-Xing; Liu, Lei; Tian, Huiping

doi:10.1007/s00033-019-1225-9

Cited by 112 publications

(25 citation statements)

References 49 publications

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“…While preparing the manuscript, we noticed some recent relevant publications on nonlinear waves, [ 74–83 ] which are, although not directly associated to

P T

symmetric non‐Hermitian systems, of special interest. In our future studies, we shall explore related nonlinear wave dynamics in

P T

symmetric non‐Hermitian systems.…”

Section: Resultsmentioning

confidence: 99%

Non‐Adiabatic Transitions in Parabolic and Super‐Parabolic PT‐Symmetric Non‐Hermitian Systems in 1D Optical Waveguides

Kam

Chen

2021

Annalen der Physik

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Exceptional points, which are spectral degeneracy points in the complex parameter space, are fundamental to non‐Hermitian quantum systems. The dynamics of non‐Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here, non‐adiabatic transitions in non‐Hermitian PT‐symmetric systems are investigated, in which the exceptional points are driven through at finite speeds which are quadratic or cubic functions of time. Different transmission dynamics separated by exceptional points are identified, and analytical approximate formulas for the non‐adiabatic transmission probabilities are derived. Possible experimental realizations with a PT‐symmetric non‐Hermitian 1D tight‐binding optical waveguide lattice are discussed through non‐Hermitian Bloch oscillations between different bands.

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“…While preparing the manuscript, we noticed some recent relevant publications on nonlinear waves, [ 74–83 ] which are, although not directly associated to

P T

symmetric non‐Hermitian systems, of special interest. In our future studies, we shall explore related nonlinear wave dynamics in

P T

symmetric non‐Hermitian systems.…”

Section: Resultsmentioning

confidence: 99%

Non‐Adiabatic Transitions in Parabolic and Super‐Parabolic PT‐Symmetric Non‐Hermitian Systems in 1D Optical Waveguides

Kam

Chen

2021

Annalen der Physik

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“…A generalized system of three-dimensional modified Kadomtsev-Petviashvili-Burgerstype equation, which describes ion-acoustic and dust-magneto-acoustic waves in one of cosmic or laboratory dusty plasmas, was studied in [2]. Moreover, in [3], the vector bright solitons of the Fokas-Lenells system, which models the femtosecond pulses in an optical fibre, was investigated. In addition, the Boussinesq-Burgers-type system of equations, which delineates shallow water waves appearing close to lakes or ocean beaches, was studied in [4].…”

Section: Introductionmentioning

confidence: 99%

“…The authors in [53] derived a Bäcklund transformation alongside a Lax pair of the form in the Calogero-Bogoyavlenskii-Schiff Equation (3) via singular manifold method. Furthermore, in [54], the authors invoked a tanh function as well as improved the (G /G)-expansion methods to construct travelling wave solutions of (3). It was also revealed that some analytic solutions secured via these methods are analogous.…”

Section: Introductionmentioning

confidence: 99%

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Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Khalique

Plaatjie

2021

Mathematics

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In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

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“…Hirota bilinear method [9] is one of the approaches to study the lump solutions. Lump solutions are completely elastic for some integrable NLPDEs [10,11,12] and others are completely inelastic [13,14,15]. Some examples of lump solutions for some integrable equations are found such as Ishimori I equation [16] and (2 +1)-dimensional extended KP equation [17].…”

Section: Introductionmentioning

confidence: 99%

Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

Elboree

2020

Math. Model. Nat. Phenom.

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In this paper, we consider the (3 + 1)-dimensional Burgers-like equation which arises in fluid mechanics, which constructed from Lax pair generating technique. The bilinear form for this model is obtained to construct the multiple-kink solutions. Lump solution, rogue wave solutions are constructed via the obtained bilinear form for this model. The physical phenomena for these solution are analyzed by studying the influence of the parameters for these solutions. The phase shifts, propagation directions and amplitudes for these solutions are controlled via these parameters. .The collisions between the lump wave and the stripe soliton, which is called lumpo solution are completely nonelastic interaction. Finally, the figures of the solutions are shown to study the dynamical behavior for the lump, rogue wave and the properties of the interaction phenomena under various parameters for (3 + 1)-dimensional Burgers-like equation. These results can't be found in the previous scientific papers.

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Vector bright solitons and their interactions of the couple Fokas–Lenells system in a birefringent optical fiber

Cited by 112 publications

References 49 publications

Non‐Adiabatic Transitions in Parabolic and Super‐Parabolic PT‐Symmetric Non‐Hermitian Systems in 1D Optical Waveguides

Non‐Adiabatic Transitions in Parabolic and Super‐Parabolic PT‐Symmetric Non‐Hermitian Systems in 1D Optical Waveguides

Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

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