Riemann–Hilbert problem associated with the vector Lakshmanan–Porsezian–Daniel model in the birefringent optical fibers

Hu, Beibei; Lin, Ji; Zhang, Ling

doi:10.1002/mma.8465

Cited by 7 publications

(4 citation statements)

References 46 publications

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“…In addition, transform t → −t and take conjugation on the kernel equation and combine the symmetry relation (17), the corresponding eigenvector for the eigenvalue…”

Section: Riemann-hilbert Problemmentioning

confidence: 99%

“…Due to the important application in nonlinear optics, abundant optical solitons [6][7][8][9][10][11] and some new exact solutions [12] for LPD equation were explored. Besides, the rich dynamic behaviors of solitons, rogue waves and the interactional solutions for a multi-component LPD equation were studied by Darboux transformation [13][14][15][16] and inverse scattering method [17].…”

Section: Introductionmentioning

confidence: 99%

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General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

Wang

Chen

2022

Nonlinear Dyn

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The inverse scattering transformation for a novel nonlocal Lakshmanan-Porsezian-Daniel (LPD) equation with rapidly decaying initial data is studied in the framework of Riemann-Hilbert problem. Firstly, a novel integrable nonlocal LPD equation corresponding to a 3 × 3 Lax pair is proposed. Secondly, the inverse scattering process with a novel left-right 3 × 3 matrix Riemann-Hilbert(RH) problem is constructed. The analytical properties and symmetry relations for the Jost functions and scattering data, which are considerably different from the local ones. Due to the special symmetry properties for the nonlocal LPD equation, the zeros of the RHP problem are purely imaginary or occur in pairs. With different types and configuration of zeros, the soliton formula are provided and the rich dynamical behaviors for the three kinds of multi-solitons for the novel nonlocal LPD equation are demonstrated. Third, by a technique of adding perturbed parameters and limiting process, the formula of higher-order solitons for the nonlocal LPD equation is exhibited. Lastly, the plots of diverse higher-order solitons and various solutions corresponding to different combinations of the following zeros: purely imaginary higher-order zeros, purely imaginary simple zeros, pairs of non-purely imaginary simple zeros and pairs of non-purely imaginary higher-order zeros are displayed.

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“…In addition, transform t → −t and take conjugation on the kernel equation and combine the symmetry relation (17), the corresponding eigenvector for the eigenvalue…”

Section: Riemann-hilbert Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

Wang

Chen

2022

Nonlinear Dyn

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“…The most important of these studies are meant to obtain soliton solutions. Many methods have been developed, including the inverse scattering transformation [7,8], the Darboux transformation [9], Bäcklund transformations [10], and Hirota's bilinear technique [11].…”

Section: Introductionmentioning

confidence: 99%

Lump-Type Solutions, Mixed Solutions and Rogue Waves for a (3+1)-Dimensional Variable-Coefficients Burgers Equation

Wu,

Cai,

Cheng

2024

Symmetry

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In this work, we consider the (3+1)-dimensional Burgers equation with variable coefficients, which is frequently used to define the motion of solitary waves. Abundant lump waves are constructed by taking the ansatz as a rational function. Furthermore, mixed solutions utilizing lump waves, rogue waves, and kink solitons are obtained by combining the rational function with an exponential function, resulting in fission and fusion phenomena.

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“…which can be obtained from the coupled LPD system with a space reduction, also has been given in [31], while the solutions of the nonlocal equation have not been studied. The coupled LPD system can depict the simultaneous propagation of the nonlinear waves in the inhomogeneous optical fiber [32][33][34][35][36][37][38][39][40][41]. Thus, the nonlocal LPD equation (1.3) governs the nonlinear wave propagation in the physical system that the coupled LPD system is related to a parity symmetry.…”

Section: Introductionmentioning

confidence: 99%

The exact solutions to a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel equation

Song,

Fang,

Zhang

et al. 2023

Nonlinear Dyn

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In this paper, we study a new type space reverse nonlocal Lakshmanan-Porserzian-Daniel (LPD) equation which can be derived from the two-component LPD system with a special reduction. We construct the multi-fold binary Darboux transformation for this equation and obtain lots of exact solutions with zero and non-zero background condition. We find that these solutions exhibit various dynamic properties, and most of the collisions between the waves in these solutions are inelastic.

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Riemann–Hilbert problem associated with the vector Lakshmanan–Porsezian–Daniel model in the birefringent optical fibers

Cited by 7 publications

References 46 publications

General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

Lump-Type Solutions, Mixed Solutions and Rogue Waves for a (3+1)-Dimensional Variable-Coefficients Burgers Equation

The exact solutions to a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel equation

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