Journal of Nonlinear Mathematical Physics

Volume 5, Issue 1, February 1998

1. On the Moyal Quantized BKP Type Hierarchies

Dolan Chapa SEN, A. Roy CHOWDHURY
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.

2. Classical and Nonclassical Symmetries of a Generalized Boussinesq Equation

M.L. GANDARIAS, M.S. BRUZON
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...

3. Symmetry of the Schrödinger Equation with Variable Potential

Wilhelm FUSHCHYCH, Zoya SYMENOH
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...

4. Stochastic Cohomology of the Frame Bundle of the Loop Space

R. LÉANDRE
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...

5. Progressive Internal Gravity Waves With Bounded Upper Surface Climbing a Triangular Obstacle

Mina B. ABD-EL-MALEK, Malak N. MAKAR
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...

6. The Integrability of Lie-invariant Geometric Objects Generated by Ideals in the Grassmann Algebra

D.L. BLACKMORE, Y.A. PRYKARPATSKY, R.V. SAMULYAK
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...

7. Lie Symmetries of Einstein's Vacuum Equations in N Dimensions

Louis MARCHILDON
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...

8. Unified approach to Miura, Bäcklund and Darboux Transformations for Nonlinear Partial Differential Equations

P.G. ESTÉVEZ, E. CONDE, P.R. GORDOA
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,...