Euler-Poincaré flows on \(\mathrm{sl}_{ n }\) opers and integrability

DOI10.1007/s10440-006-9078-6zbMath1119.35076OpenAlexW2075278191MaRDI QIDQ870486

Partha Guha

Publication date: 12 March 2007

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-006-9078-6

zbMATH Keywords

Boussinesq equationRiccati equationcoupled KdV equationsHirota-Satsuma equationDrienfield-Sokolov equationopers

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Applications of local differential geometry to the sciences (53B50)

Related Items (3)

Reciprocal link for a coupled Camassa-Holm type equation ⋮ Goldman algebra, opers and the swapping algebra ⋮ Variations along the Fuchsian locus

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lie algebras and equations of Korteweg-de Vries type
• Coadjoint orbits of the Virasoro group
• Kähler structures on K-orbits of the group of diffeomorphisms of the circle
• Korteweg - de Vries suoerequation as an Euler equation
• Modifying Lax equations and the second Hamiltonian structure
• Unitary representations of some infinite dimensional groups
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Indicators of an entire function and the regularity of the growth of the Fourier coefficients of the logarithm of its modulus
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Extension of the Virasoro and Neveu-Schwarz algebras and generalized Sturm-Liouville operators
• On the Poisson geometry of the Adler-Gel'fand-Dikii brackets
• Spectral curves, opers and integrable systems.
• Symplectic structures of the spaces of projective and affine curves
• Antiplectic structure, diffeomorphism and generalized KdV family
• Locally projective spaces of dimension one
• PROJECTIVE CONNECTIONS, AGD MANIFOLD AND INTEGRABLE SYSTEMS
• Diffeomorphisms on S¹, projective structures and integrable systems
• Solitons and the removal of eigenvalues for fourth-order differential operators
• Commuting flows and conservation laws for Lax equations
• Factorization of operators I. Miura transformations
• ON ANTIPLECTIIC PAIRS IN THE HAMILITONIAN FORMALISM OF EVOLUTION EQUATIONS
• The geometry of the KdV equation
• Lectures on Mechanics
• Invariant differential equations and the Adler–Gel’fand–Dikii bracket
• Space of linear differential operators on the real line as a module over the Lie algebra of vector fields
• SPACE OF HIGHER ORDER DIFFERENTIAL OPERATORS ON S¹ AND INTEGRABLE FLOWS
• On the quasi-Hamiltonian formalism of the KdV equation
• \(\text{Diff}(S^1)\) and Adler-Gelfand-Dikii spaces and integrable systems

This page was built for publication: Euler-Poincaré flows on \(\mathrm{sl}_{ n }\) opers and integrability