Exact quasi-periodic solutions to the sine(sinh)-Gordon equations: The method for computation and analysis
arXiv:2501.07862 · doi:10.1016/j.physd.2026.135141
Abstract
The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the -functions that uniformize the associated spectral curve. Quasi-periodic solutions to the sine(sinh)-Gordon equations are obtained in terms of the function , reality conditions are revised, and a method of computation and analysis is presented. The proposed method is designed to analyze solutions by means of the Hamiltonian technique, which is illustrated in genera one and two.
42 pages, 11 figures