Volume 9, Issue 3, April 2001

H GARGOUBI

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 [7]). 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 main...

D B FAIRLIE

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 weight...

Steinar EVJE, Kenneth H KARLSEN

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, f =...

Ugurhan MU GAN, Fahd JRAD

Pages: 282 - 310

Starting from the second Painlevé equation, we obtain Painlevé type equations of higher order by using the singular point analysis.

Mattias LIEFVENDAHL, Gunilla KREISS

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,...

Hervé LEBLOND

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 multiscale...

Dmitry ROYTENBERG

Pages: 347 - 356

We compute the Poisson cohomology of the one-parameter family of SU(2)-covariant Poisson structures on the homogeneous space S2 = CP1 = SU(2)/U(1), where SU(2) is endowed with its standard PoissonLie group structure, thus extending the result of Ginzburg [2] on the BruhatPoisson structure which is...

P BRACKEN, A M GRUNDLAND

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...