Reduction groups and related integrable difference systems of NLS type
arXiv:1503.06406 · doi:10.1063/1.4928048
Abstract
We extend the reduction group method to the Lax-Darboux schemes associated with nonlinear Schrödinger type equations. We consider all possible finite reduction groups and construct corresponding Lax operators, Darboux transformations, hierarchies of integrable differential-difference equations, integrable partial difference systems and associated scalar partial difference equations.
arXiv comment25 pages
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- Darboux transformation with Dihedral reduction group
- Entwining Yang-Baxter maps related to NLS type equations
- Yang--Baxter maps, Darboux transformations, and linear approximations of refactorisation problems
- Difference systems in bond and face variables and non-potential versions of discrete integrable systems
- Local Yang--Baxter correspondences and set-theoretical solutions to the Zamolodchikov tetrahedron equation
- Darboux transformations with tetrahedral reduction group and related integrable systems
- Algebro-geometric solutions to the lattice potential modified Kadomtsev--Petviashvili equation
- Algebraic entropy for systems of quad equations
- Discrete integrable systems, Darboux transformations, and Yang-Baxter maps