## SciPost Submission Page

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

### by O. Babelon, K. K. Kozlowski, V. Pasquier

#### - Published as SciPost Phys. 5, 035 (2018)

### 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.
Baxter T-Q equation
Non-linear integral equations (NLIE)
Thermodynamic Bethe Ansatz (TBA)
Toda chains

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