Equivalent forms of multi component Toda hierarchies

DOI10.1016/j.geomphys.2010.11.013zbMath1233.37037OpenAlexW2119343422WikidataQ57436472 ScholiaQ57436472MaRDI QIDQ631655

A. V. Opimakh, Aloysius G. Helminck, Gerardus F. Helminck

Publication date: 14 March 2011

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2010.11.013

zbMATH Keywords

bilinear formLax equationsinfinite-dimensional Cauchy problemlower and upper triangular \({\mathbb Z}\times {\mathbb Z}\)-matrices

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Group structures and generalizations on infinite-dimensional manifolds (58B25) Lattice dynamics; integrable lattice equations (37K60)

Cites Work

• Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials
• The relative frame bundle of an infinite-dimensional flag variety and solutions of integrable hierarchies
• Moving poles of meromorphic linear systems on \(\mathbb P^{1}(\mathbb C)\) in the complex plane
• Fermionic construction of the partition function for multimatrix models and the multicomponent Toda lattice hierarchy
• The equivariant Gromov-Witten theory of \(\mathbb P^1\)
• Melting crystal, quantum torus and Toda hierarchy
• The Zero Curvature Form of Integrable Hierarchies in the ℤ × ℤ-Matrices
• Sur La Classification Des Fibres Holomorphes Sur La Sphere de Riemann
• Commuting flows and conservation laws for Lax equations
• Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture
• Integrals of nonlinear equations of evolution and solitary waves
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