Abstract
Two integrable symplectic maps are constructed through nonlinearization of the discrete linear spectral problems in the Lax pair of the Hirota equation, i.e. the lattice sine-Gordon equation. As an application, these maps are used to calculate the finite genus solutions of the Hirota equation and the closely related lattice potential MKdV equation, i.e. the special H3 model in the Adler–Bobenko–Suris list.
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