Volume 5, Issue 1, February 1998
Pages: 1 - 7
Quantization of BKP type equations are done through the Moyal bracket and the
formalism of pseudo-differential operators. It is shown that a variant of the dressing
operator can also be constructed for such quantized systems.
Pages: 8 - 12
We apply the Lie-group formalism and the nonclassical method due to Bluman and
Cole to deduce symmetries of the generalized Boussinesq equation, which has the
classical Boussinesq equation as an special case. We study the class of functions f(u)
for which this equation admit either the classical or...
Pages: 13 - 22
We study symmetry properties of the Schrödinger equation with the potential as a
new dependent variable, i.e., the transformations which do not change the form of
the class of equations. We also consider systems of the Schrödinger equations with
certain conditions on the potential. In addition we...
Pages: 23 - 40
We study the differential forms over the frame bundle of the based loop space. They
are stochastics in the sense that we put over this frame bundle a probability measure.
In order to understand the curvatures phenomena which appear when we look at the
Lie bracket of two horizontal vector fields, we...
Pages: 41 - 53
In this paper we discuss a theoretical model for the interfacial profiles of progressive
non-linear waves which result from introducing a triangular obstacle, of finite height,
attached to the bottom below the flow of a stratified, ideal, two layer fluid, bounded
from above by a rigid boundary. The...
Pages: 54 - 67
We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant
geometric objects studied before by E.Cartan. Especially, the E.Cartan theory is
enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame
work of the Wahlquist Estabrook prolongation structures...
Pages: 68 - 81
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with
a cosmological term. For this purpose, we first write down the second prolongation
of the symmetry generating vector fields, and compute its action on Einstein's equations. Instead of setting to zero the coefficients...
Pages: 82 - 114
This paper is an attempt to present and discuss at some length the Singular Manifold Method. This Method is based upon the Painlevé Property systematically used
as a tool for obtaining clear cut answers to almost all the questions related with
Nonlinear Partial Differential Equations: Lax pairs, Miura,...