A Fully Noncommutative Painlevé II Hierarchy: Lax Pair and Solutions Related to Fredholm Determinants
نویسندگان
چکیده
We consider Fredholm determinants of matrix Hankel operators associated to versions the n-th Airy functions. Using theory integrable operators, we relate them a fully noncommutative Painlevé II hierarchy, defined through matrix-valued version Lenard operators. In particular, Riemann-Hilbert techniques used study these allows find Lax pair for each member hierarchy. Finally, coefficients matrices are explicitly written in terms and some solutions hierarchy square
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ژورنال
عنوان ژورنال: Symmetry Integrability and Geometry-methods and Applications
سال: 2021
ISSN: ['1815-0659']
DOI: https://doi.org/10.3842/sigma.2021.002