A finite genus solution of the H1 model

The H1 model in the Adler–Bobenko–Suris list, i.e. the lattice potential KdV equation and the closely related lattice KdV equation with Nijhoff’s discretization, are investigated. A new Lax pair of the H1 model is given, by which integrable symplectic maps are constructed through a non-linearization procedure. Resorting to these maps, finite genus solutions of the H1 model as well as the lattice KdV equation are calculated.