Journal of Nonlinear Mathematical Physics

Let F(Sn ) be the space of tensor densities on Sn of degree . We consider this space as an induced module of the nonunitary spherical series of the group SO0(n+1, 1) and classify (so(n+1, 1), SO(n+1))-simple and unitary submodules of F(Sn ) as a function of .

We observe a correspondence between the zero modes of superconformal algebras S (2, 1) and W(4) ([8]) and the Lie superalgebras formed by classical operators apearing in the Kähler and hyper-Kähler geometry.

We study non-trivial deformations of the natural action of the Lie algebra Vect(Rn ) on the space of differential forms on Rn . We calculate abstractions for integrability of ifinitesimal multi-parameter deformations and determine the commutative associative algebra corresponding to the miniversal deformation...

Various solutions are displayed and analyzed (both analytically and numerically) of a recently-introduced many-body problem in the plane which includes both integrable and nonintegrable cases (depending on the values of the coupling constants); in paticular the origin of certain periodic behaviors is...

We present a geometric description, based on the affine Weyl group E (1) 6 , of two discrete analogues of the Painlevé VI equation, known as the asymmetric q-PV and asymmetric d-PIV. This approach allows us to describe in a unified way the evolution of the mapping along the independent variable and along...

We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative...

It is shown that in the case of multicomponent integrable systems connected with algebras An, the discrete transformation T possesses the fine structure and can be represented in the form T = Tli i , where Ti are n commuting basis discrete transfomations and li are arbitrary natural numbers. All the...