# Solution of Baxter equation for the $q$-Toda and Toda$\_2$ chains by NLIE

Source: [Solution of Baxter equation for the $q$-Toda and Toda$\_2$ chains by NLIE](<https://www.sota2.com/research/paper/68fa38971e209131ce8bba54>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T23:02:41.357Z

Authors: O. Babelon, K. K. Kozlowski, V. Pasquier

Published: 2018-04-05T09:33:47.000Z

## Abstract

We construct a basis of solutions of the scalar $\\boldsymbol{ \\texttt{t} }- \\boldsymbol{ \\texttt{Q} }$ equation describing the spectrum of the $q$-Toda and Toda$\_2$ chains by using auxiliary non-linear integral equations. Our construction allows us to provide quantisation conditions for the spectra of these models in the form of thermodynamic Bethe Ansatz-like equations.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1804.01749>)

[PDF](<https://arxiv.org/pdf/1804.01749.pdf>)