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
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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…
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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…
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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
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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
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Entwining Yang–Baxter maps related to NLS type equations
- MathematicsJournal of Physics A: Mathematical and Theoretical
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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…
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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
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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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