Isospectral flow in loop algebras and quasiperiodic solutions of the sine-Gordon equation

DOI10.1063/1.530041zbMath0780.35100arXivhep-th/9210077OpenAlexW2070285670MaRDI QIDQ3141356

J. Harnad, M. A. Wisse

Publication date: 6 February 1994

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

Full work available at URL: https://arxiv.org/abs/hep-th/9210077

zbMATH Keywords

sine-Gordon equationloop algebraHamiltonian frameworkAdler-Kostant-Symes theoremLiouville-Arnold integration method

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) KdV equations (Korteweg-de Vries equations) (35Q53) Applications of global differential geometry to the sciences (53C80) Invariance and symmetry properties for PDEs on manifolds (58J70) Theta functions and curves; Schottky problem (14H42)

Related Items (5)

Why the general Zakharov-Shabat equations form a hierarchy ⋮ Classical and quantum integrable systems in \(\widetilde{\mathfrak gl}(2)^{+*}\) and separation of variables ⋮ Quantization of solitons and the restricted sine-Gordon model ⋮ On Separation of Variables for Integrable Equations of Soliton Type ⋮ Separation of variables for soliton equations via their binary constrained flows

Cites Work

• Real two-zone solutions of the sine-Gordon equation
• Numerical inverse spectral transform for the periodic sine-Gordon equation: Theta function solutions and their linearized stability
• A particle-system model of the sine-Gordon hierarchy
• Isospectral Hamiltonian flows in finite and infinite dimensions. I: Generalized Moser systems and moment maps into loop algebras
• The solution to a generalized Toda lattice and representation theory
• Systems of Toda type, inverse spectral problems, and representation theory
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Isospectral Hamiltonian flows in finite and infinite dimensions. II: Integration of flows
• Theta functions and non-linear equations
• REAL ELLIPTIC SOLUTIONS OF THE "SINE-GORDON" EQUATION
• Hamiltonian Formalism for Nonlinear SchrÖDinger Equations and Sine-Gordon Equations
• The sine-gordon and sinh-gordon equations on the circle
• Spectral theory for the periodic sine-Gordon equation: A concrete viewpoint

This page was built for publication: Isospectral flow in loop algebras and quasiperiodic solutions of the sine-Gordon equation