Journal of Nonlinear Mathematical Physics

Volume 8, Issue 3, August 2001

1. Solving the Difference Initial-Boundary Value Problems by the Operator Exponential Method

I M NEFEDOV, I A SHERESHEVSKII
Pages: 313 - 324
We suggest a modification of the operator exponential method for the numerical soling the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions as the peturbation of the same operator for periodic ones. We...

2. Volume Preserving Multidimensional Integrable Systems and Nambu­Poisson Geometry

Partha GUHA
Pages: 325 - 341
In this paper we study generalized classes of volume preserving multidimensional intgrable systems via Nambu­Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close resemblance to the self dual Einstein equation. All these dispersionless...

3. A Tree of Linearisable Second-Order Evolution Equations by Generalised Hodograph Transformations

Norbert EULER, Marianna EULER
Pages: 342 - 362
We present a list of (1+1)-dimensional second-order evolution equations all connected via a proposed generalised hodograph transformation, resulting in a tree of equations transformable to the linear second-order autonomous evolution equation. The list includes autonomous and nonautonomous equations.

4. Dark Equations

B A KUPERSHMIDT
Pages: 363 - 445
Observing the Universe, astronomers have concluded that the motion of stars can not be accounted for unless one assumes that most of the mass in the Universe is carried on by a "dark matter", so far impervious to all attempts at being detected. There is now a similar concept of "dark energy". I shall...