Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations

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dc.creatorKiselev, Arthemy V.
dc.creatorWolf, Thomas
dc.date2005-11-24
dc.date2006-02-28
dc.date.accessioned2026-07-07T09:34:21Z
dc.date.available2026-07-07T09:34:21Z
dc.descriptionWe construct new integrable coupled systems of N=1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian structures. A fermionic extension of the Burgers equation is related with the Burgers flows on associative algebras. A Gardner's deformation is found for the bosonic super-field dispersionless Boussinesq equation, and unusual properties of a recursion operator for its Hamiltonian symmetries are described. Also, we construct a three-parametric supersymmetric system that incorporates the Boussinesq equation with dispersion and dissipation but never retracts to it for any values of the parameters.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0511071
dc.identifierhttp://arxiv.org/abs/math-ph/0511071
dc.identifierSIGMA 2 (2006), 030, 19 pages
dc.identifierdoi:10.3842/SIGMA.2006.030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159465
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectExactly Solvable and Integrable Systems
dc.subject35Q53; 37K05; 37K10; 37K35; 58A50; 81T40
dc.titleSupersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations
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