Differential operators on the superline, Berezinians, and Darboux transformations

DOI10.1007/s11005-017-0958-7zbMath1394.16027arXiv1605.07286OpenAlexW3102434188MaRDI QIDQ2410930

Simon S. Li, Ekaterina Shemyakova, Theodore Th. Voronov

Publication date: 20 October 2017

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.07286

zbMATH Keywords

intertwining relationDarboux transformationdressing transformationBereziniansuperlinesuper Wronskian

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Rings of differential operators (associative algebraic aspects) (16S32) Analysis on supermanifolds or graded manifolds (58C50) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (13)

An Algebraic Background for Hierarchies of PDE in Dimension (2|1) ⋮ On the differential equation of first and second order in the Zeon algebra ⋮ On super cluster algebras based on super Plücker and super Ptolemy relations ⋮ Laplace maps and constraints for a class of third-order partial differential operators ⋮ On the second order differential equation involving two ordinary and one para-Grassmann variable ⋮ Differential operators on the algebra of densities and factorization of the generalized Sturm-Liouville operator ⋮ Classification of multidimensional Darboux transformations: first order and continued type ⋮ Binary Darboux transformations of the supersymmetric Heisenberg magnet model ⋮ Factorization of Darboux-Laplace transformations for discrete hyperbolic operators ⋮ Laplace invariants of differential operators ⋮ Classification of Darboux transformations for operators of the form \(\partial_x\partial_y+a\partial_x+b\partial_y+c\) ⋮ On super Plücker embedding and cluster algebras ⋮ Darboux transformations and Fay identities for the extended bigraded Toda hierarchy

Cites Work

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• Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
• Differential transformations of parabolic second-order operators in the plane
• A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy
• Vector fields and differential equations on supermanifolds
• Dressing chains and the spectral theory of the Schrödinger operator
• Factorization of differential operators, quasideterminants, and nonabelian Toda field equations
• Lagrangian chains and canonical Bäcklund transformations
• On the Darboux transformation of \(N\)th order
• On the structure of singularities of integrable Schrödinger operators
• Darboux transformations for supersymmetric Korteweg-de Vries equations
• On the theory of Laplace-Darboux transformations
• Darboux transformation, factorization, and supersymmetry in one-dimensional quantum mechanics
• Supercurves, their Jacobians, and super KP equations
• Berezinians, exterior powers and recurrent sequences
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• Darboux transformations for differential operators on the superline
• Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
• The infinite-dimensional dressing dynamical system
• Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds
• On the singularities of potentials of exactly soluble Schrödinger equations and on Hadamard's problem
• Proof of the Completeness of Darboux Wronskian Formulae for Order Two
• Invariants for Darboux Transformations of Arbitrary Order for $$\mathcal{D}_x\mathcal{D}_y+a\mathcal{D}_x+b\mathcal{D}_y+c$$
• ASSOCIATED STURM-LIOUVILLE SYSTEMS

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