Journal of Nonlinear Mathematical Physics

Peter E Hydon: Symmetry Methods for Differential Equations: A Beginner's Guide Cambridge Texts in Applied Mathematics, Cambridge University Press, 2000.

An N = (2|2) superfield formulation of the N = (1|1) supersymmetric Toda lattice hierarchy is proposed, and its five real forms are presented.

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 tetrahedra.

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...

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 does...

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 series:...

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 (at )t = (-1)p(a) a, where p(a) is the parity of a, and let L(at ) = L(a). Then A admits a nondegenerate supersymmetric invariant bilinear form...

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 with...

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...

It is shown that one system of coupled KdV equations, found in J. Nonlin. Math. Phys.,