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

### Submission summary

 As Contributors: Karol Kozlowski Arxiv Link: https://arxiv.org/abs/1804.01749v3 Date accepted: 2018-10-08 Date submitted: 2018-06-21 Submitted by: Kozlowski, Karol Submitted to: SciPost Physics Discipline: Physics Subject area: Mathematical Physics Approach: Theoretical

### 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.

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 5, 035 (2018)

### Author comments upon resubmission

We thank the referee for his comments. We have taken all of them into account.

### List of changes

All has been implemented.

### Submission & Refereeing History

Resubmission 1804.01749v3 on 21 June 2018
Submission 1804.01749v2 on 21 May 2018