Hyperelliptic theta-functions and spectral methods: KdV and KP solutions

DOI10.1007/s11005-006-0068-4zbMath1127.14032arXivnlin/0512066OpenAlexW2039083522MaRDI QIDQ2457226

Christian Klein, Jörg Frauendiener

Publication date: 30 October 2007

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0512066

zbMATH Keywords

theta functionhyperelliptic Riemann surfaceKorteweg--de Vries equationKadomtsev--Petviashvili equationnumerical evaluation of solutions of nonlinear equations

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) KdV equations (Korteweg-de Vries equations) (35Q53) Computation of special functions and constants, construction of tables (65D20) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Theta functions and curves; Schottky problem (14H42)

Related Items (18)

A numerical study on the \(N\)-periodic wave solutions of two coupled bilinear equations ⋮ On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation ⋮ A Riemann-Hilbert problem for the finite-genus solutions of the KdV equation and its numerical solution ⋮ 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 ⋮ Computation of large-genus solutions of the Korteweg-de Vries equation ⋮ On computing high-dimensional Riemann theta functions ⋮ A numerical study of the 3-periodic wave solutions to KdV-type equations ⋮ Algebraic Curves and Riemann Surfaces in Matlab ⋮ Cylindrical Kadomtsev-Petviashvili equation: old and new results ⋮ A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations ⋮ Damping to prevent the blow-up of the Korteweg-de Vries equation ⋮ Computation of the topological type of a real Riemann surface ⋮ Computational approach to hyperelliptic Riemann surfaces ⋮ Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: computational results ⋮ Efficient computation of the branching structure of an algebraic curve ⋮ Numerical evaluations of periodic wave solutions, integrable time discretization and their applications to the mKdV–sine-Gordon equation

Uses Software

• CARS

Cites Work

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