Integrable Quantum Mappings and Quantization Aspects of Integrable Discrete-time Systems
F.W. Nijhoff, H.W. Capel (Clarkson University)
TL;DR
This paper explores the quantum Yang-Baxter structure in non-ultralocal lattice models, analyzing integrable quantum mappings, and provides explicit examples related to lattice KdV and MKdV equations with their quantum invariants.
Contribution
It introduces a canonical framework for integrable quantum mappings in non-ultralocal models and presents explicit solutions with quantum invariants for lattice KdV and MKdV systems.
Findings
Established a quantum Yang-Baxter structure for non-ultralocal models
Constructed explicit quantum mappings for lattice KdV and MKdV equations
Derived exact quantum invariants for these mappings
Abstract
We study a quantum Yang-Baxter structure associated with non-ultralocal lattice models. We discuss the canonical structure of a class of integrable quantum mappings, i.e. canonical transformations preserving the basic commutation relations. As a particular class of solutions we present two examples of quantum mappings associated with the lattice analogues of the KdV and MKdV equations, together with their exact quantum invariants. plain LaTeX, equations.sty appended
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra