On Hamiltonian systems integrable in elliptic functions that describe waves over underwater banks and ridges

Abstract

We discuss the 4-dimensional Hamiltonian systems that describe waves over underwater banks and ridges. The systems are exactly integrable in terms of elliptic functions and of solutions to nontrivial transcendental equations involving the elliptic integrals (Weierstrass' $\zeta$-function).

LaTeX, 6 pages