Discretizations of the generalized AKNS scheme

10 May 2020 Doikou Anastasia Sklaveniti Spyridoula

We consider space discretizations of the matrix Zakharov-Shabat AKNS scheme, in particular the discrete matrix non-linear Scrhr\"odinger (DNLS) model, and the matrix generalization of the Ablowitz-Ladik (AL) model, which is the more widely acknowledged discretization. We focus on the derivation of solutions via local Darboux transforms for both discretizations, and we derive novel solutions via generic solutions of the associated discrete linear equations... (read more)

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Categories


  • MATHEMATICAL PHYSICS
  • HIGH ENERGY PHYSICS - THEORY
  • MATHEMATICAL PHYSICS
  • EXACTLY SOLVABLE AND INTEGRABLE SYSTEMS