• Corpus ID: 207780033

Riemann-Hilbert approach and soliton solutions for the higher-order dispersive nonlinear Schrödinger equation with nonzero boundary conditions

@article{Li2019RiemannHilbertAA,
  title={Riemann-Hilbert approach and soliton solutions for the higher-order dispersive nonlinear Schr{\"o}dinger equation with nonzero boundary conditions},
  author={Zhi-qiang Li and Shou‐Fu Tian and Jin-Jie Yang},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2019}
}
In this work, the higher-order dispersive nonlinear Schrodinger equation with non-zero boundary conditions at infinity is investigated including the simple and double zeros of the scattering coefficients. We introduce a appropriate Riemann surface and uniformization variable in order to deal with the double-valued functions occurring in the process of direct scattering. Then, the direct scattering problem is analyzed involving the analyticity, symmetries and asymptotic behaviors. Moreover, for… 

Figures from this paper

Riemann-Hilbert approach to the inhomogeneous fifth-order nonlinear Schrödinger equation with non-vanishing boundary conditions

We consider the inhomogeneous fifth-order nonlinear Schrodinger (ifoNLS) equation with nonzero boundary condition in detailed. Firstly, the spectral analysis of the scattering problem is carried out.

Riemann-Hilbert approach to the generalized variable-coefficient nonlinear Schrödinger equation with non-vanishing boundary conditions

In this work, we consider the generalized variable-coefficient nonlinear Schrodinger equation with non-vanishing boundary conditions at infinity including the simple and double poles of the

Riemann-Hilbert problem for the sextic nonlinear Schr\"{o}dinger equation with non-zero boundary conditions

We consider a matrix Riemann-Hilbert problem for the sextic nonlinear Schrodinger equation with a non-zero boundary conditions at infinity. Before analyzing the spectrum problem, we introduce a

The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: Inverse scattering transform and multisoliton solutions

Abstract We study the inverse scattering transform of the general fifth-order nonlinear Schrödinger (NLS) equation with nonzero boundary conditions (NZBCs), which can be reduced to several integrable

Riemann-Hilbert Approach and N-Soliton Solutions For Three-Component Coupled Hirota Equations

In this work, we consider an integrable three-component coupled Hirota (tcCH) equations in detail via the Riemann-Hilbert (RH) approach. We present some properties of the spectral problems of the

Riemann-Hilbert approach and $N$-soliton solutions for a new four-component nonlinear Schr\"odinger equation

A new four-component nonlinear Schr\"{o}dinger equation is first proposed in this work and studied by Riemann-Hilbert approach. Firstly, we derive a Lax pair associated with a $5\times5$ matrix

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

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

Asymptotic stage of modulation instability for a fourth-order dispersive nonlinear Schr¨odinger equation with nonzero boundary conditions

In this work, we consider the long-time asymptotics for the Cauchy problem of a fourth-order dispersive nonlinear Schr¨odinger equation with nonzero boundary conditions at infinity. Firstly, in order

References

SHOWING 1-10 OF 52 REFERENCES

Riemann–Hilbert problem for the modified Landau–Lifshitz equation with nonzero boundary conditions

We study a matrix Riemann–Hilbert (RH) problem for the modified Landau–Lifshitz (mLL) equation with nonzero boundary conditions at infinity. In contrast to the case of zero boundary conditions,

Riemann-Hilbert approach for the NLSLab equation with nonzero boundary conditions

We consider the inverse scattering transform for the nonlinear Schr\"{o}dinger equation in laboratory coordinates (NLSLab equation) with nonzero boundary conditions (NZBCs) at infinity. In order to

Inverse scattering transform and soliton solutions for the focusing Kundu-Eckhaus equation with nonvanishing boundary conditions.

The focusing Kundu-Eckhaus (KE) equation with non-zero boundary conditions at infinity, under two cases: simple zeros and double zeros, is investigated systematically via Riemann-Hilbert (RH)

Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions

The inverse scattering transform for an integrable discretization of the defocusing nonlinear Schrodinger equation with nonvanishing boundary values at infinity is constructed. This problem had been

Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions

The inverse scattering transform for the focusing nonlinear Schrodinger equation with non-zero boundary conditions at infinity is presented, including the determination of the analyticity of the

Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

A nonlocal nonlinear Schrödinger (NLS) equation was recently introduced and shown to be an integrable infinite dimensional Hamiltonian evolution equation. In this paper a detailed study of the

Conservation laws, soliton solutions and modulational instability for the higher-order dispersive nonlinear Schrödinger equation

AbstractIn this paper, analytically investigated is a higher-order dispersive nonlinear Schrödinger equation. Based on the linear eigenvalue problem associated with this equation, the integrability
...