A genus six cyclic tetragonal reduction of the Benney equations

Abstract

A reduction of Benney's equations is constructed corresponding to Schwartz-Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian sigma-function of the curve.

39pages, 3figures

References in corpus (3)

• Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times
• Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians
• Abelian functions associated with a cyclic tetragonal curve of genus six

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• Some New Addition Formulae for Weierstrass Elliptic Functions
• Building Abelian Functions with Generalised Baker-Hirota Operators