Volume 9, Issue 3, August 2002
Pages: 248 - 255
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...
Pages: 256 - 261
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...
Pages: 261 - 281
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,...
Pages: 282 - 310
Starting from the second Painlevé equation, we obtain Painlevé type equations of
higher order by using the singular point analysis.
Pages: 311 - 324
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,...
Pages: 325 - 346
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...
Pages: 347 - 356
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...
Pages: 357 - 381
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...