Finite genus solutions to the lattice Schwarzian Korteweg-de Vries equation

Abstract

Based on integrable Hamiltonian systems related to the derivative Schwarzian Korteweg-de Vries (SKdV) equation, a novel discrete Lax pair for the lattice SKdV (lSKdV) equation is given by two copies of a Darboux transformation which can be used to derive an integrable symplectic correspondence. Resorting to the dis- crete version of Liouville-Arnold theorem, finite genus solutions to the lSKdV equation are calculated through Riemann surface method.

Keywords:

• lattice Schwarzian Korteweg-de Vries equation
• integrable symplectic map
• finite genus solution

2000 Mathematics Subject Classification:

• 37J10
• 37K10
• 39A13