Abstract
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.
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