The Toda hierarchy and the KdV hierarchy
Copyright policy )The Toda hierarchy and the KdV hierarchy
The Toda hierarchy of size $N$ is well known to be analogous to the KdV hierarchy at $N$ goes to infinity. This paper shows that given $f$ a periodic function, there is a canonical way of defining the initial data for the Toda lattice equations so that the evolution of this data under the Toda lattice hierarchy looks asymptotically like the evolution of $f$ under the KdV hierarchy. Further, the conserved quantities of $f$ and those of the Toda hierarchy match.
AMSTeX
- University of California, Los Angeles United States
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, KdV flows, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), periodic Toda hierarchies, Mathematics - Algebraic Geometry, 58F07, 35Q53, Other completely integrable PDE, periodic KdV hierarchy, FOS: Mathematics, Algebraic Geometry (math.AG), Toda flow
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, KdV flows, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), periodic Toda hierarchies, Mathematics - Algebraic Geometry, 58F07, 35Q53, Other completely integrable PDE, periodic KdV hierarchy, FOS: Mathematics, Algebraic Geometry (math.AG), Toda flow
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