Symmetries and recursion operators for classical and supersymmetric differential equations
General Material Designation
[Book]
First Statement of Responsibility
/ by I.S. Krasil?shchik and P.H.M. Kersten
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Dordrecht ; Boston ; London
Name of Publisher, Distributor, etc.
: Kluwer Academic,
Date of Publication, Distribution, etc.
, c2000.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
xvi, 384 p. , ill. , 25 cm.
SERIES
Series Title
(Mathematics and its applications
Volume Designation
; v. 507)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references (p. 373-378) and index.
CONTENTS NOTE
Text of Note
4. Supersymmetric extensions of the KdV equation, N = 2 -- Ch. 8. Symbolic computations in differential geometry. 1. Super (graded) calculus. 2. Classical differential geometry. 3. Overdetermined systems of PDE.
Text of Note
1. C-cohomologies of partial differential equations. 2. Spectral sequences and graded evolutionary derivations. 3. C-cohomologies of evolution equations. 4. From deformations to recursion operators. 5. Deformations of the Burgers equation. 6. Deformations of the KdV equation. 7. Deformations of the nonlinear Schrodinger equation. 8. Deformations of the classical Boussinesq equation. 9. Symmetries and recursion for the Sym equation -- Ch. 6. Super and graded theories. 1. Graded calculus. 2. Graded extensions. 3. Nonlocal theory and the case of evolution equations. 4. The Kupershmidt super KdV equation. 5. The Kupershmidt super mKdV equation. 6. Supersymmetric KdV equation. 7. Supersymmetric mKdV equation. 8. Supersymmetric extensions of the NLS. 9. Concluding remarks -- Ch. 7. Deformations of supersymmetric equations. 1. Supersymmetric KdV equation. 2. Supersymmetric extensions of the NLS equation. 3. Supersymmetric Boussinesq equation.
Text of Note
Ch. 1. Classical symmetries. 1. Jet spaces. 2. Nonlinear PDE. 3. Symmetries of the Burgers equation. 4. Symmetries of the nonlinear diffusion equation. 5. The nonlinear Dirac equations. 6. Symmetries of the self-dual SU(2) Yang-Mills equations -- Ch. 2. Higher symmetries and conservation laws. 1. Basic structures. 2. Higher symmetries and conservation laws. 3. The Burgers equation. 4. The Hilbert - Cartan equation. 5. The classical Boussinesq equation -- Ch. 3. Nonlocal theory. 1. Coverings. 2. Nonlocal symmetries and shadows. 3. Reconstruction theorems. 4. Nonlocal symmetries of the Burgers equation. 5. Nonlocal symmetries of the KDV equation. 6. Symmetries of the massive Thirring model. 7. Symmetries of the Federbush model. 8. Backlund transformations and recursion operators -- Ch. 4. Brackets. 1. Differential calculus over commutative algebras. 2. Frolicher - Nijenhuis bracket. 3. Structure of symmetry algebras -- Ch. 5. Deformations and recursion operators.
SERIES
Title
Mathematics and its applications (Kluwer Academic Publishers)