Journal of Nonlinear Mathematical Physics

Volume 9, Issue 3, April 2001

1. Algebra gl(lambda) Inside the Algebra of Differential Operators on the Real Line

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...

2. A Universal Solution

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...

3. An Error Estimate for Viscous Approximate Solutions of Degenerate Parabolic Equations

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 =...

4. Painlevé Test and Higher Order Differential Equations

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.

5. Bounds for the Threshold Amplitude for Plane Couette Flow

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,...

6. Higher Order Terms in Multiscale Expansions: A Linearized KdV Hierarchy

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...

7. Poisson Cohomology of SU(2)-Covariant "Necklace" Poisson Structures on S2

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...

8. Solutions of the Generalized Weierstrass Representation in Four-Dimensional Euclidean Space

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...