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

Abstract

We 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.

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (5)

• On the local systems Hamiltonian in the weakly nonlocal Poisson brackets
• Hamiltonian operators and l*-coverings
• Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I
• Locality of symmetries generated by nonhereditary, inhomogeneous, and time-dependent recursion operators: a new application for formal symmetries
• (Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation

Cited by in corpus (4)

• Classification of integrable super-systems using the SsTools environment
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment
• On weakly non-local, nilpotent, and super-recursion operators for N=1 super-equations