## 8 Citations

### Multi-component AKNS systems

- Mathematics
- 2022

We study two members of the multi-component AKNS hierarchy. These are multi-NLS and multi-MKdV systems. We derive the Hirota bilinear forms of these equations and obtain soliton solutions. We ﬁnd all…

### Integrability of local and nonlocal non-commutative fourth order quintic NLS equations

- Mathematics
- 2020

We prove integrability of a generalised non-commutative fourth order quintic NLS equation. The proof is relatively succinct and rooted in the linearisation method pioneered by Ch. Poppe. It is based…

### Integrability of local and nonlocal non-commutative fourth order quintic nonlinear Schrodinger equations

- Mathematics
- 2020

Abstract. We prove integrability of a generalised non-commutative fourth order quintic nonlinear Schrödinger equation. The proof is relatively succinct and rooted in the linearisation method…

### The non-commutative Korteweg–de Vries hierarchy and combinatorial Pöppe algebra

- MathematicsPhysica D: Nonlinear Phenomena
- 2022

### Applications of Grassmannian flows to integrable systems

- Mathematics
- 2019

We show how many classes of partial differential systems with local and nonlocal nonlinearities are linearisable in the sense that they are realisable as Fredholm Grassmannian flows. In other words,…

## References

SHOWING 1-10 OF 31 REFERENCES

### Complete integrability of Nonlocal Nonlinear Schr\"odinger equation

- Mathematics
- 2015

Based on the completeness relation for the squared solutions of the Lax operator $L$ we show that a subset of nonlocal equations from the hierarchy of nonlocal nonlinear Schrodinger equations (NLS)…

### Nonlocal Nonlinear Schr\"odinger Equations and Their Soliton Solutions

- Mathematics, Physics
- 2017

We study standard and nonlocal nonlinear Schrodinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal…

### Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy

- Mathematics, Physics
- 2018

In this paper, nonlocal reductions of the Ablowitz–Kaup–Newell–Suger (AKNS) hierarchy are collected, including the nonlocal nonlinear Schrödinger hierarchy, nonlocal modified Korteweg‐de Vries…

### Integrable Nonlocal Reductions

- Mathematics, Physics
- 2018

We present some nonlocal integrable systems by using the Ablowitz-Musslimani nonlocal reductions. We first present all possible nonlocal reductions of nonlinear Schr\"{o}dinger (NLS) and modified…

### Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform

- Mathematics, Physics
- 2016

### Transformations between Nonlocal and Local Integrable Equations

- Mathematics, Physics
- 2017

Recently, a number of nonlocal integrable equations, such as the PT ‐symmetric nonlinear Schrödinger (NLS) equation and PT ‐symmetric Davey–Stewartson equations, were proposed and studied. Here, we…

### Soliton solutions for the nonlocal nonlinear Schrödinger equation

- Physics
- 2016

Abstract.The Darboux transformation (DT) for the integrable nonlocal nonlinear Schrödinger equation (nNLSE) is constructed with the aid of loop group method. Based on the DT, we derive several types…

### Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation

- Physics, Mathematics
- 2017

In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915–946 (2016)] is gauge equivalent to a…

### Rogue waves and rational solutions of the Hirota equation.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

The Darboux transformation technique is modified to show how to construct the hierarchy of rational solutions of the Hirota equation, a modified nonlinear Schrödinger equation that takes into account higher-order dispersion and time-delay corrections to the cubic nonlinearity.