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An algebraic approach to discrete time integrability
Anastasia Doikou, Iain Findlay
We propose the systematic construction of classical and quantum two dimensional space-time lattices primarily based on algebraic considerations, i.e. on the existence of associated…
Time-like boundary conditions in the NLS model
Anastasia Doikou, Iain Findlay, Spyridoula Sklaveniti
We focus on the non-linear Schrodinger model and we extend the notion of space-time dualities in the presence of integrable time-like boundary conditions. We identify the associate…
Solitons: conservation laws & dressing methods
Anastasia Doikou, Iain Findlay
We review some of the fundamental notions associated to the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and als…
A Dual Construction of the Isotropic Landau-Lifshitz Model
Iain Findlay
By interchanging the roles of the space and time coordinates, we describe a dual construction of the isotropic Landau-Lifshitz model, providing equal-space Poisson brackets and dua…
Non-commutative NLS-type hierarchies: dressing & solutions
Anastasia Doikou, Iain Findlay, Spyridoula Sklaveniti
We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PD…