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Peter E Hydon: Symmetry Methods for Differential Equations: A Beginner's Guide
Cambridge Texts in Applied Mathematics, Cambridge University Press, 2000.
Pages: 183 - 195
An N = (2|2) superfield formulation of the N = (1|1) supersymmetric Toda lattice
hierarchy is proposed, and its five real forms are presented.
Pages: 196 - 210
An invariant of three-dimensional orientable manifolds is built on the base of a slution of pentagon equation expressed in terms of metric characteristics of Euclidean
Pages: 211 - 216
We present here the explicit parametric solutions of second order differential equations
invariant under time translation and rescaling and third order differential equations
invariant under time translation and the two homogeneity symmetries. The computtion of first integrals gives in the most general...
Pages: 217 - 219
The singularity analysis is carried out for a system of four first-order quadratic ODEs
with a parameter, which was proposed recently by Golubchik and Sokolov. A transfomation of dependent variables is revealed by the analysis, after which the transformed
system possesses the Painlevé property and...
Pages: 220 - 228
Among simple Z-graded Lie superalgebras of polynomial growth, there are several
which have no Cartan matrix but, nevertheless, have a quadratic even Casimir element
C2: these are the Lie superalgebra kL
(1|6) of vector fields on the (1|6)-dimensional
supercircle preserving the contact form, and the...
Pages: 229 - 255
Let A be an associative simple (central) superalgebra over C and L an invariant
linear functional on it (trace). Let a at
be an antiautomorphism of A such that
a, where p(a) is the parity of a, and let L(at
) = L(a). Then A admits
a nondegenerate supersymmetric invariant bilinear...
Pages: 256 - 287
This is the second part of a series of papers dealing with an extensive class of anlytic difference operators admitting reflectionless eigenfunctions. In the first part, the
pertinent difference operators and their reflectionless eigenfunctions are constructed
from given "spectral data", in analogy...
Pages: 288 - 310
We obtain the collection of symmetric and symplectic matrix integrals and the colletion of Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke,
as specific elements in the Spin-group orbit of the vacuum vector of a fermionic Fock
space. This fermionic Fock space is the same...
Pages: 311 - 312
It is shown that one system of coupled KdV equations, found in J. Nonlin. Math. Phys.,