# Low-$T$ asymptotic expansion of the solution to the Yang-Yang equation

Source: [Low-$T$ asymptotic expansion of the solution to the Yang-Yang equation](<https://www.sota2.com/research/paper/68fa2ec21e209131ce865f34>)

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

Data updated: 2025-10-27T03:28:03.737Z

Authors: K. K. Kozlowski

Published: 2011-12-28T23:15:00.000Z

## Abstract

We prove that the unique solution to the Yang-Yang equation arising in the context of the thermodynamics of the so-called non-linear Schr\\"{o}dinger model admits a low-temperature expansion to all orders. Our approach provides a rigorous justification, for a certain class of non-linear integral equations, of the low-temperature asymptotic expansion that were argued previously in various works related to the low-temperature behavior of integrable models.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1112.6199>)

[PDF](<https://arxiv.org/pdf/1112.6199.pdf>)