# Nonlocal general vector nonlinear Schrödinger equations: Integrability, PT symmetribility, and solutions

@article{Yan2016NonlocalGV, title={Nonlocal general vector nonlinear Schr{\"o}dinger equations: Integrability, PT symmetribility, and solutions}, author={Zhenya Yan}, journal={Appl. Math. Lett.}, year={2016}, volume={62}, pages={101-109} }

## 47 Citations

### General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system.

- MathematicsChaos
- 2019

It is shown that the complex-amplitude stationary solutions can yield a wide class of complex and time-independent PT-symmetric potentials, and the symmetry breaking does not occur in the PT-Symmetric linear system with the associated potentials.

### Integrable Nonlocal PT Symmetric and Reverse Space-Time Nonlinear Schrödinger Equations

- Mathematics, Physics
- 2018

In this chapter a review of recent advances related to the emerging field of integrable nonlocal nonlinear PT symmetric, reverse space-time and reverse time only equations is presented. Starting from…

### Riemann–Hilbert approach and soliton classification for a nonlocal integrable nonlinear Schrödinger equation of reverse-time type

- MathematicsNonlinear Dynamics
- 2021

In this paper, a Riemann–Hilbert (RH) approach is reported for a physically meaningful nonlocal integrable nonlinear Schrödinger equation of reverse-time type, which is connected with a special…

### Riemann–Hilbert approach and soliton classification for a nonlocal integrable nonlinear Schrödinger equation of reverse-time type

- MathematicsNonlinear Dynamics
- 2021

In this paper, a Riemann–Hilbert (RH) approach is reported for a physically meaningful nonlocal integrable nonlinear Schrödinger equation of reverse-time type, which is connected with a special…

### The nonlinear Schrödinger equation with generalized nonlinearities and PT-symmetric potentials: Stable solitons, interactions, and excitations.

- Physics, MathematicsChaos
- 2017

The nonlinear Schrödinger equation with generalized nonlinearities and complex non-Hermitian potentials is investigated and it is found that the nonlinearity can excite the unstable linear modes to stable nonlinear modes.

### A unified inverse scattering transform and soliton solutions of the nonlocal mKdV equation with non-zero boundary conditions

- Mathematics
- 2019

In this paper, we present a systematical theory of a unified and simple inverse scattering transform for both focusing and defocusing nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV)…

### A unified inverse scattering transform and soliton solutions of the nonlocal modified KdV equation with non-zero boundary conditions

- Mathematics
- 2018

We present a rigorous theory of a unified and simple inverse scattering transform (IST) for both focusing and defocusing real nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations…

### Integrability, Darboux transformation and exact solutions for nonlocal couplings of AKNS equations

- MathematicsAppl. Math. Lett.
- 2021

### A unified inverse scattering transform for the nonlocal modified KdV equation with non-zero boundary conditions.

- Mathematics
- 2018

We present a rigorous theory of a unified and simple inverse scattering transform (IST) for both focusing and defocusing real nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations…

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