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

Download

10.3842:SIGMA.2006.030.pdf

Date

2006-2-28

Author

KISELEV, Arthemy V.
WOLF, Thomas

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

113
views

77
downloads

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.

Subject Keywords

Mathematical Physics, Geometry and Topology, Analysis

URI

https://hdl.handle.net/11511/50923

Journal

Symmetry, Integrability and Geometry: Methods and Applications

DOI

https://doi.org/10.3842/sigma.2006.030

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

Ermakov's Superintegrable Toy and Nonlocal Symmetries Leach, P. G. L.; Karasu, Emine Ayşe; Nucci, M. C.; Andriopoulos, K. (SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 2005-01-01) We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the comp...
Equivariant cross sections of complex Stiefel manifolds Onder, T (Elsevier BV, 2001-01-16) Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W-k(M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier re...
Time-dependent recursion operators and symmetries Gurses, M; Karasu, Atalay; Turhan, R (Informa UK Limited, 2002-05-01) The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional integrable evolution equations are considered. It has been previously observed hat he symmetries of he integrable evolution equations obtained through heir recursion operators do not satisfy the symmetry equations. There have been several attempts to resolve his problem. It is shown that in the case of time-dependent evolution equations or time-dependent recursion operators associativity is lost. Due to this fact such recursion ope...
On homotopy groups of real algebraic varieties and their complexifications Ozan, Yıldıray (Springer Science and Business Media LLC, 2004-10-01) Let X-0 be a topological component of a nonsingular real algebraic variety and i : X --> X-C is a nonsingular projective complexification of X. In this paper, we will study the homomorphism on homotopy groups induced by the inclusion map i: X-0 --> X-C and obtain several results using rational homotopy theory and other standard tools of homotopy theory.
Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential, Wei-Hua Potential, Varshni Potential Arda, Altug; Sever, Ramazan (Walter de Gruyter GmbH, 2014-03-01) Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any K-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n, K).

Citation Formats

A. V. KISELEV and T. WOLF, “Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations,” Symmetry, Integrability and Geometry: Methods and Applications, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/50923.