The Lie algebra gl() with C, introduced by B L Feigin, can be embedded into
the Lie algebra of differential operators on the real line (see ). We give an explicit
formula of the embedding of gl() into the algebra D of differential operators on the
space of tensor densities of degree on R. Our...
The phenomenon of an implicit function which solves a large set of second order
partial differential equations obtainable from a variational principle is explicated by
the introduction of a class of universal solutions to the equations derivable from an
arbitrary Lagrangian which is homogeneous of...
Relying on recent advances in the theory of entropy solutions for nonlinear (strongly)
degenerate parabolic equations, we present a direct proof of an L1
error estimate for
viscous approximate solutions of the initial value problem for
tw + div V (x)f(w) = A(w),
where V = V (x) is a vector field,...
We prove nonlinear stability for finite amplitude perturbations of plane Couette flow.
A bound of the solution of the resolvent equation in the unstable complex half-plane
is used to estimate the solution of the full nonlinear problem. The result is a lower
bound, including Reynolds number dependence,...
We consider a wide class of model equations, able to describe wave propagation in
dispersive nonlinear media. The Korteweg-de Vries (KdV) equation is derived in this
general frame under some conditions, the physical meanings of which are clarified.
It is obtained as usual at leading order in some...
We compute the Poisson cohomology of the one-parameter family of SU(2)-covariant
Poisson structures on the homogeneous space S2
= SU(2)/U(1), where SU(2)
is endowed with its standard PoissonLie group structure, thus extending the result
of Ginzburg  on the BruhatPoisson structure which...
Several classes of solutions of the generalized Weierstrass system, which induces costant mean curvature surfaces into four-dimensional Euclidean space are constructed.
A gauge transformation allows us to simplify the system considered and derive fatorized classes of solutions. A reduction of the generalized...