Diffeomorphisms on S1, projective structures and integrable systems

DOI10.1017/S1446181100008026zbMath1003.35109MaRDI QIDQ3146207

Partha Guha

Publication date: 24 November 2002

Published in: The ANZIAM Journal (Search for Journal in Brave)

zbMATH Keywords

Korteweg-de Vries equationSchwarzian KdV equationHamiltonian flowAdler-Gelfand-Dikii operator

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (6)

Symmetry reductions and exact solutions of two new generalized negative KdV type equations ⋮ Euler-Poincaré flows on \(\mathrm{sl}_{ n }\) opers and integrability ⋮ Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit ⋮ Invariance of second order ordinary differential equations under two-dimensional affine subalgebras of Ermakov-Pinney Lie algebra ⋮ SPACE OF HIGHER ORDER DIFFERENTIAL OPERATORS ON S¹ AND INTEGRABLE FLOWS ⋮ Geodesics and submanifold structures in conformal geometry

Uses Software

• AGD

Cites Work

• Symplectic leaves of the Gel'fand-Dikij brackets and homotopy classes of nondegenerate curves
• Coadjoint orbits of the Virasoro group
• Korteweg - de Vries suoerequation as an Euler equation
• Unitary representations of some infinite dimensional groups
• 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
• On a Schwarzian PDE associated with the KdV hierarchy
• Symplectic structures of the spaces of projective and affine curves
• Diffeomorphism, periodic KdV and C. Neumann system
• PROJECTIVE CONNECTIONS, AGD MANIFOLD AND INTEGRABLE SYSTEMS
• Hamiltonian Formalism for Nonlinear SchrÖDinger Equations and Sine-Gordon Equations
• The geometry of the KdV equation
• On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket
• 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
• SL(n + 1)-invariant equations which reduce to equations of Korteweg-de Vries type
• On the quasi-Hamiltonian formalism of the KdV equation

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