A genus six cyclic tetragonal reduction of the Benney equations
نویسندگان
چکیده
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 σ-function of the curve.
منابع مشابه
Abelian Functions Associated with a Cyclic Tetragonal Curve of Genus Six
We develop the theory of Abelian functions defined using a tetragonal curve of genus six, with the specific example of the cyclic curve, y = x + λ4x + λ3x + λ2x + λ1x + λ0 discussed in detail. We define generalisations of the Weierstrass σ and ℘ functions, along with additional classes of Abelian functions. In addition, we present the associated partial differential equations satisfied by the f...
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