Riemann–Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions

Ma, Wen‐Xiu

doi:10.1007/s40314-018-0703-6

Cited by 31 publications

(20 citation statements)

References 39 publications

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“…We begin with the spatial and temporal equations of the spectral problems, with the associated Lax pair {U, V }: [11]…”

Section: Six-component Akns Hierarchy Of Coupled Six-order Integrable...mentioning

confidence: 99%

Riemann-Hilbert problems of a non-local reverse-time AKNS system of six-order and dynamical behaviours of $N$-soliton

Ahmed,

Adjiri

2022

Preprint

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In this paper, we are going to solve nonlinear nonlocal reverse-time six-component six-order AKNS system. We used reverse-time reduction to reduce the coupled system to an integrable six-order NLS-type equation. Starting from the spectral problem of the AKNS system, a Riemann-Hilbert problem will be formulated. This formulation allows to generate soliton solutions by using the vectors lying in the kernel of the matrix Jost solutions. When reflection coefficients are zeros, the jump matrix is identity and the corresponding Riemann-Hilbert problem yields soliton solutions, leading to explore their dynamics.

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“…We begin with the spatial and temporal equations of the spectral problems, with the associated Lax pair {U, V }: [11]…”

Section: Six-component Akns Hierarchy Of Coupled Six-order Integrable...mentioning

confidence: 99%

Riemann-Hilbert problems of a non-local reverse-time AKNS system of six-order and dynamical behaviours of $N$-soliton

Ahmed,

Adjiri

2022

Preprint

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“…in which the matrix M is given by (22), and ν k = (ν k,1 , ν k,2 , · · · , ν k,N +1 ) T andν k = (ν k,1 ,ν k,2 , · · · ,ν k,N +1 ), 1 ≤ k ≤ n, are determined by (19) and (20). As a particular reduction, we now take N = 3 in Eqs.…”

Section: Soliton Solutionsmentioning

confidence: 99%

Construction of Multi-soliton Solutions of the N-Coupled Hirota Equations in an Optical Fiber^*

Kang¹,

Xia²

2019

Chinese Phys. Lett.

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This paper focuses on investigation of the N -coupled Hirota equations arising in an optical fiber. Starting from analyzing the spectral problem, a kind of matrix Riemann-Hilbert problem is formulated strictly on the real axis. Then based on the resulting matrix Riemann-Hilbert problem under the constraint of no reflection, multi-soliton solutions to the N -coupled Hirota equations are presented explicitly.

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“…On the other hand, some of the higher-order spectral problems have to be transformed into RH problem. This approach, developed by Zakharov et al [34], was successively applied to various integrable systems with a single component [3][4][5][8][9][10][11][12][13][16][17][18][19][20][21][24][25][26][27][28][29][30]32,33,[35][36][37][38]. However, to the best of authors' knowledge, only a few studies deal with multi-component problems.…”

Section: Introductionmentioning

confidence: 99%

The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation

Zhou¹

2021

EAJAM

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A four-component nonlinear Schrödinger equation associated with a 5×5 Lax pair is investigated. A spectral problem is analysed and the Jost functions are used in order to derive a Riemann-Hilbert problem connected with the equation under consideration. N-soliton solutions of the equation are obtained by solving the Riemann-Hilbert problem without reflection. For N = 1 and N = 2, the local structure and dynamic behavior of some special solutions is analysed by invoking their graphic representations.

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Riemann–Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions

Cited by 31 publications

References 39 publications

Riemann-Hilbert problems of a non-local reverse-time AKNS system of six-order and dynamical behaviours of $N$-soliton

Riemann-Hilbert problems of a non-local reverse-time AKNS system of six-order and dynamical behaviours of $N$-soliton

Construction of Multi-soliton Solutions of the N-Coupled Hirota Equations in an Optical Fiber^*

The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation

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Riemann–Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions

Cited by 31 publications

References 39 publications

Riemann-Hilbert problems of a non-local reverse-time AKNS system of six-order and dynamical behaviours of $N$-soliton

Riemann-Hilbert problems of a non-local reverse-time AKNS system of six-order and dynamical behaviours of $N$-soliton

Construction of Multi-soliton Solutions of the N-Coupled Hirota Equations in an Optical Fiber*

The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation

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Construction of Multi-soliton Solutions of the N-Coupled Hirota Equations in an Optical Fiber^*