Holomorphic, rational Lax pairs of a q-discrete Painlevé VI equation

Q: What type of study is this?

This is a Quantitative Study study.

Robert Conte

doi:10.48550/arxiv.2510.03435

October 3, 2025Open Access

Holomorphic, rational Lax pairs of a q-discrete Painlevé VI equation

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Key Points

Matrix Lax pairs are established for the q-discrete Painlevé VI equation, enhancing theoretical understanding.
The findings show that the two eigenvalues of the monodromy matrix at infinity can be equal without losing validity.
Elements of the Lax pairs are rational functions of the dependent variables, allowing for novel solutions.
This work highlights potential applications in integrable systems and complex analysis.

Implication

Analysis constructs holomorphic Lax pairs for the q-discrete Painlevé VI equation, suggesting new insights on eigenvalues behavior.

Abstract

We build several matrix Lax pairs of q-PVI valid even when the two eigenvalues of the residue of the monodromy matrix at infinity are equal. Their elements are rational functions of the dependent variables.

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Cite This Study

Robert Conte (2025) studied this question.

synapsesocial.com/papers/68e861b07ef2f04ca37e4bfc https://doi.org/10.48550/arxiv.2510.03435

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Holomorphic, rational Lax pairs of a q-discrete Painlevé VI equation

Key Points

Implication

Abstract

Discussion

Cite This Study

Holomorphic, rational Lax pairs of a q-discrete Painlevé VI equation

Key Points

Implication

Abstract

Discussion

Cite This Study

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