A finite genus solution of the Hirota equation via integrable symplectic maps (Q2879927)

This paper describes two integrable symplectic maps which are constructed through nonlinearlization of discrete linear spectral problems in the Lax pair of the Hirota equation. The integrable Hamiltonian system generated through nonlinearization of the linear spectral problem is introduced, as well as the lattice sine-Gordon equation and the lattice potential MKdV equation. Two integrable symplectic maps \(S_\beta\) and \(S_\gamma\) are constructed and solutions of the Hirota equation expressed by the Abel-Jacobi variable are presented. In addition, finite genus solutions via \(S_{\beta_1}\) and \(S_{\beta_2}\) are derived.