# 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…

## 14 Citations

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

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- 2020

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

- Mathematics
- 2020

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

- Mathematics
- 2020

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

- MathematicsTheoretical and Mathematical Physics
- 2022

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…

### Inverse scattering transform of an extended nonlinear Schrödinger equation with nonzero boundary conditions and its multisoliton solutions

- MathematicsJournal of Mathematical Analysis and Applications
- 2020

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

- MathematicsEast Asian Journal on Applied Mathematics
- 2020

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

- Mathematics
- 2020

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

- Mathematics
- 2021

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

- Mathematics
- 2022

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…

### Soliton and breather solutions for a fifth-order modified KdV equation with a nonzero background

- Physics, MathematicsAppl. Math. Lett.
- 2020

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