Commutative partial differential operators

DOI10.1016/S0167-2789(01)00159-2zbMath0980.35141arXivmath/9907097MaRDI QIDQ5940198

Alex Kasman, Emma Previato

Publication date: 29 July 2001

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9907097

zbMATH Keywords

Darboux transformationsdifferential resultantsgeneralization of the Burchnall-Chaundy problemmaximal-commutative rings

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Soliton equations (35Q51) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items (8)

Burchnall-Chaundy polynomials for matrix ODOs and Picard-Vessiot theory ⋮ The Schur-Sato theory for quasi-elliptic rings ⋮ Differential elimination with Dixon resultants ⋮ Unnamed Item ⋮ Algebraic Geometric Properties of Spectral Surfaces of Quantum Integrable Systems and Their Isospectral Deformations ⋮ Factorization and resultants of partial differential operators ⋮ The resultant on compact Riemann surfaces ⋮ The algebraic integrability of the quantum Toda lattice and the Radon transform

Cites Work

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• Integration of nonlinear equations by the methods of algebraic geometry
• Kernel inspired factorizations of partial differential operators
• Quantum integrable systems and differential Galois theory
• \(\mathcal{D}\)-modules and Darboux transformations
• Commutative rings of partial differential operators and Lie algebras
• Darboux transformations of bispectral quantum integrable systems
• Commuting Partial Differential Operators and Vector Bundles Over Abelian Varieties

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