Rank three representations of Painlev\'e systems: II. de Rham structure, Fourier--Laplace transformation
Miklos Eper, Szilard Szabo
TL;DR
This paper explores the Fourier--Laplace transformation connecting rank 3 and rank 2 D-module representations of Painlevé systems, revealing a biregular morphism between their de Rham structures using microlocalization.
Contribution
It introduces a formal microlocalization approach to describe the Fourier--Laplace transformation in Painlevé systems and establishes a biregular morphism between their de Rham complexes.
Findings
Established a Fourier--Laplace transformation between rank 3 and rank 2 D-modules.
Proved the existence of a biregular morphism between de Rham structures.
Applied microlocalization techniques to Painlevé systems.
Abstract
We use formal microlocalization to describe the Fourier--Laplace transformation between rank 3 and rank 2 D-module representations of Painleve systems. We conclude the existence of biregular morphism between the corresponding de Rham complex structures.
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Taxonomy
TopicsNonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models