Integrability of reductions of the discrete KdV and potential KdV equations

Abstract

We study the integrability of mappings obtained as reductions of the discrete Korteweg-de Vries (KdV) equation and of two copies of the discrete potential Korteweg-de Vries equation (pKdV). We show that the mappings corresponding to the discrete KdV equation, which can be derived from the latter, are completely integrable in the Liouville-Arnold sense. The mappings associated with two copies of the pKdV equation are also shown to be integrable.

22 pages, 1 figure

References in corpus (1)

• Discrete integrable systems and Poisson algebras from cluster maps

Cited by in corpus (6)

• Some integrable maps and their Hirota bilinear forms
• On Reductions of the Hirota-Miwa Equation
• On some classes of discrete polynomials and ordinary difference equations
• Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation
• On the singularity structure of the discrete KdV equation
• Poisson structures for difference equations