On the Riemann theta function of a trigonal curve and solutions of the Boussinesq and KP equations

DOI10.1007/BF00403466zbMath0641.35061OpenAlexW2162073723WikidataQ57936929 ScholiaQ57936929MaRDI QIDQ1100638

Aleksandr Olegovich Smirnov, Vladimir B. Matveev

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1007/bf00403466

zbMATH Keywords

Riemann theta function KP equation Boussinesq equations hyperelliptic Riemann surfaces completely integrable algebro-geometrical superposition principles

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (34)

ALGEBRO-GEOMETRIC SOLUTIONS OF THE BOUSSINESQ HIERARCHY ⋮ Quasi-periodic solutions to the hierarchy of four-component Toda lattices ⋮ Algebro-geometric integration of a modified shallow wave hierarchy ⋮ A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation ⋮ The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices ⋮ Quasi-periodic solutions of the Kaup-Kupershmidt hierarchy ⋮ Riemann theta function solutions of the Caudrey-Dodd-Gibbon-Sawada-Kotera hierarchy ⋮ Algebro-geometric quasi-periodic solutions to the Satsuma-Hirota hierarchy ⋮ Quasi-periodic solutions of a discrete integrable equation with a finite-dimensional integrable symplectic structure ⋮ The coupled Sasa–Satsuma hierarchy: Trigonal curve and finite genus solutions ⋮ Action-angle variables for the Lie-Poisson Hamiltonian systems associated with Boussinesq equation ⋮ Riemann surface and Riemann theta function solutions of the discrete integrable hierarchy ⋮ Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy ⋮ Star-triangle equations and some properties of algebraic curves connected with the integrable chiral Potts model ⋮ Elliptic solutions of the Korteweg-de Vries equation ⋮ Riemann theta function solutions to the coupled long wave-short wave resonance equations ⋮ Finite genus solutions to the coupled Burgers hierarchy ⋮ A note on the quasi-periodic solutions of the modified Boussinesq hierarchy ⋮ Finite-band solutions for the hierarchy of coupled Toda lattices ⋮ Application of the trigonal curve to the Blaszak-Marciniak lattice hierarchy ⋮ The application of trigonal curve theory to the second-order Benjamin-Ono hierarchy ⋮ The application of trigonal curve to the Mikhailov-Shabat-Sokolov flows ⋮ The application of the theory of trigonal curves to the discrete coupled nonlinear Schrödinger hierarchy ⋮ Explicit quasi-periodic solutions of the Vakhnenko equation ⋮ A generalization of Baker's quadratic formulae for hyperelliptic \(\wp\)-functions ⋮ Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions ⋮ Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy ⋮ Algebro-geometric integration of the modified Belov-Chaltikian lattice hierarchy ⋮ Some comments on the solvable chiral Potts model ⋮ On a class of elliptic solutions of the Boussinesq equations ⋮ Quasi-Periodic Solutions of Nonlinear Evolution Equations Associated with a 3 × 3 Matrix Spectral Problem ⋮ Three-sheeted Riemann surface and solutions of the Itoh–Narita–Bogoyavlensky lattice hierarchy ⋮ A New Approach to the Boussinesq Hierarchy ⋮ Algebro-geometric solutions to the modified Sawada-Kotera hierarchy

This page was built for publication: On the Riemann theta function of a trigonal curve and solutions of the Boussinesq and KP equations