# 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 (pdf) Date accepted: 2018-10-08 Date submitted: 2018-06-21 02:00 Submitted by: Kozlowski, Karol Submitted to: SciPost Physics Academic field: Physics Specialties: Atomic, Molecular and Optical Physics - Experiment 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

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Published as SciPost Phys. 5, 035 (2018)

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

### List of changes

All has been implemented.