Hyperelliptic theta-functions and spectral methods

DOI10.1016/j.cam.2003.10.003zbMath1052.65107arXivnlin/0512065OpenAlexW2016508220MaRDI QIDQ1877133

Christian Klein, Jörg Frauendiener

Publication date: 16 August 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0512065

zbMATH Keywords

numerical examplesEinstein equationsRiemann surfaceErnst equationspectral methodshyperelliptic theta-functions

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Computation of special functions and constants, construction of tables (65D20) Other functions coming from differential, difference and integral equations (33E30) Hypoelliptic equations (35H10) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Numerical approximation and evaluation of special functions (33F05)

Related Items (17)

A numerical study on the \(N\)-periodic wave solutions of two coupled bilinear equations ⋮ On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation ⋮ New construction of algebro-geometric solutions to the Camassa–Holm equation and their numerical evaluation ⋮ Efficient computation of multidimensional theta functions ⋮ Computational approach to compact Riemann surfaces ⋮ A numerical study of the 3-periodic wave solutions to KdV-type equations ⋮ Algebraic Curves and Riemann Surfaces in Matlab ⋮ Hyperelliptic theta-functions and spectral methods: KdV and KP solutions ⋮ Cylindrical Kadomtsev-Petviashvili equation: old and new results ⋮ Interactions of dispersive shock waves ⋮ A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations ⋮ Computation of the topological type of a real Riemann surface ⋮ On linear degeneracy of integrable quasilinear systems in higher dimensions ⋮ Computational approach to hyperelliptic Riemann surfaces ⋮ Numerical study of a multiscale expansion of the Korteweg–de Vries equation and Painlevé-II equation ⋮ Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models ⋮ Efficient computation of the branching structure of an algebraic curve

Uses Software

• CARS

Cites Work

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• A Practical Guide to Pseudospectral Methods
• Periods of hyperelliptic integrals expressed in terms of θ -constants by means of Thomae formulae
• General Relativity
• Computing Riemann matrices of algebraic curves

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