# Integrable discretisations for a class of nonlinear Schrodinger equations on Grassmann algebras

@article{Grahovski2013IntegrableDF, title={Integrable discretisations for a class of nonlinear Schrodinger equations on Grassmann algebras}, author={Georgi G. Grahovski and Alexander V. Mikhailov}, journal={Physics Letters A}, year={2013}, volume={377}, pages={3254-3259} }

## 26 Citations

A discrete Darboux–Lax scheme for integrable difference equations

- MathematicsChaos, Solitons & Fractals
- 2022

Darboux transformations, discrete integrable systems and related Yang-Baxter maps

- Mathematics
- 2014

Darboux transformations constitute a very important tool in the theory of integrable systems. They map trivial solutions of integrable partial differential equations to non-trivial ones and they link…

Constructing soliton solutions and super-bilinear form of lattice supersymmetric Kdv equation

- Physics
- 2015

The Hirota bilinear form and multisoliton solution for semidiscrete and fully discrete (difference–difference) versions of the supersymmetric Korteweg–de Vries (KdV) equation found by Xue et al (2013…

A noncommutative discrete potential KdV lift

- MathematicsJournal of Mathematical Physics
- 2018

In this paper, we construct a Grassmann extension of a Yang-Baxter map which first appeared in [16] and can be considered as a lift of the discrete potential Korteweg-de Vries (dpKdV) equation. This…

This is a repository copy of Grassmann extensions of Yang-Baxter maps

- Mathematics
- 2018

In this paper we show that there are explicit Yang-Baxter maps with Darboux-Lax representation between Grassmann extensions of algebraic varieties. Motivated by some recent results on noncommutative…

Backlund{Darboux Transformations and Discretizations of Super KdV Equation

- Physics, Mathematics
- 2014

For a generalized super KdV equation, three Darboux transformations and the corresponding Backlund transformations are constructed. The compatibility of these Darboux transformations leads to three…

Grassmann extensions of Yang-Baxter maps

- Mathematics
- 2015

In this paper we show that there are explicit Yang-Baxter maps with Darboux-Lax representation between Grassmann extensions of algebraic varieties. Motivated by some recent results on noncommutative…

Entwining Yang–Baxter maps related to NLS type equations

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

We construct birational maps that satisfy the parametric set-theoretical Yang–Baxter equation and its entwining generalisation. For this purpose, we employ Darboux transformations related to…

Integrable extensions of Adler's map via Grassmann algebras

- Mathematics
- 2020

We study certain extensions of the Adler map on Grassmann algebras Γ(n) of order n. We consider a known Grassmann-extended Adler map, and assuming that n = 1 we obtain a commutative extension of…

A Supersymmetric AKNS Problem and Its Darboux‐Bäcklund Transformations and Discrete Systems

- Mathematics
- 2015

In this paper, we consider a supersymmetric AKNS spectral problem. Two elementary and a binary Darboux transformations are constructed. By means of reductions, Darboux and Bäcklund transformations…

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