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

We investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann–Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix.

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Dynamic Behaviors of Soliton Solutions for a Three-Coupled Lakshmanan-Porsezian-Daniel Model

10.21203/rs.3.rs-883566/v1 ◽

2021 ◽

Author(s):

Beibei Hu ◽

Ji Lin ◽

Ling Zhang

Keyword(s):

Spectral Analysis ◽

Fourth Order ◽

Soliton Solutions ◽

Lax Pair ◽

Nonlinear Dynamical ◽

Jump Matrix ◽

Dynamical Behaviors ◽

Helical Protein ◽

Order Dispersion ◽

Dispersion Term

Abstract In this paper, we use the Riemann-Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan-Porsezian-Daniel (LPD) model, which describe the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a 4×4 unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.

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

Computational and Applied Mathematics ◽

10.1007/s40314-018-0703-6 ◽

2018 ◽

Vol 37 (5) ◽

pp. 6359-6375 ◽

Cited By ~ 14

Author(s):

Wen-Xiu Ma

Keyword(s):

Fourth Order ◽

Soliton Solutions ◽

Akns System

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FINDING THE EXACT SOLITON SOLUTIONS OF NONLINEAR FOURTH-ORDER EQUATION OF THE GENERALIZED HIROTA-SATSUMA COUPLED WITH KdV

Journal of Pure and Applied Mathematics Advances and Applications ◽

10.18642/jsata_7100121368 ◽

2015 ◽

Vol 13 (1) ◽

pp. 1-14

Keyword(s):

Fourth Order ◽

Soliton Solutions ◽

Order Equation ◽

Fourth Order Equation ◽

Exact Soliton Solutions

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Inverse Scattering and Soliton Solutions of Nonlocal Complex Reverse-Spacetime Modified Korteweg-de Vries Hierarchies

Symmetry ◽

10.3390/sym13030512 ◽

2021 ◽

Vol 13 (3) ◽

pp. 512

Author(s):

Liming Ling ◽

Wen-Xiu Ma

Keyword(s):

Inverse Scattering ◽

Soliton Solutions ◽

Identity Matrix ◽

Nonlocal Symmetry ◽

Scattering Problems ◽

Spectral Problems ◽

Symmetry Reductions ◽

Jump Matrix ◽

De Vries ◽

Scattering Transforms

This paper aims to explore nonlocal complex reverse-spacetime modified Korteweg-de Vries (mKdV) hierarchies via nonlocal symmetry reductions of matrix spectral problems and to construct their soliton solutions by the inverse scattering transforms. The corresponding inverse scattering problems are formulated by building the associated Riemann-Hilbert problems. A formulation of solutions to specific Riemann-Hilbert problems, with the jump matrix being the identity matrix, is established, where eigenvalues could equal adjoint eigenvalues, and thus N-soliton solutions to the nonlocal complex reverse-spacetime mKdV hierarchies are obtained from the reflectionless transforms.

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