Toda-Darboux maps and vertex operators
M. Adler, P. van Moerbeke

TL;DR
This paper investigates Toda-Darboux transforms for Toda lattice operators, showing how they induce transformations on tau-vectors via vertex operators and on eigenfunctions through Wronskians, enriching the understanding of integrable systems.
Contribution
It introduces a novel framework connecting Toda-Darboux transforms with vertex operators and Wronskians, providing new insights into the structure of integrable systems.
Findings
Toda-Darboux transforms induce tau-vector transformations via vertex operators
Eigenfunctions are transformed through Wronskian relations
The framework links Darboux transforms with integrable system symmetries
Abstract
The purpose of this paper is to study Toda-Darboux transforms, i.e., Darboux transforms for operators L(t) flowing according to the Toda lattice. Each element of the null-space specifies a factorization for all t and thus a Toda-Darboux transform on . The Toda-Darboux map induces a transformation on the tau-vectors, given by a certain vertex operator, and on eigenfunctions, given by a Wronskian. .
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Topics in Algebra · Advanced Algebra and Geometry
