Kernel inspired factorizations of partial differential operators

DOI10.1006/jmaa.1999.6383zbMath0934.35027OpenAlexW1965771308MaRDI QIDQ1301879

Alex Kasman

Publication date: 2 April 2000

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1999.6383

zbMATH Keywords

Darboux transformationNullstellensatzquantum integrabilitybispectralityrational-exponential function

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) General theory of PDEs and systems of PDEs with constant coefficients (35E20) Commutative rings of differential operators and their modules (13N10)

Related Items (3)

Factorization of a Matrix Differential Operator Using Functions in Its Kernel ⋮ On factoring an operator using elements of its kernel ⋮ Commutative partial differential operators

Cites Work

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• Differential equations in the spectral parameter
• Bispectral Darboux transformations: The generalized Airy case
• Formal solutions and factorization of differential operators with power series coefficients
• Darboux transformations from \(n\)-KdV to KP
• Factorization of differential operators with rational functions coefficients
• Quantum integrable systems and differential Galois theory
• \(\mathcal{D}\)-modules and Darboux transformations
• Integrability in the theory of Schrödinger operator and harmonic analysis
• Commutative rings of partial differential operators and Lie algebras
• Darboux transformations of bispectral quantum integrable systems
• Spectral difference equations satisfied by KP soliton wavefunctions
• The duality of the generalized Calogero and Ruijsenaars problems
• New situation in quantum mechanics (wonderful potentials from the inverse problem)

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