Symmetry Properties of a Generalized Korteweg-de Vires Equation and some Explicit Solutions

The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invarint solution for it are obtained by means of this technique. Polynomial, trigonometric and elliptic function solutions can be calculated. It is shown that this generalized equation can be reduced to a first-order equation under a particular second-order differential constraint which resembles a Schrodinger equation. For a particular instance in which the constraint is satisfied, the generalized equation is reduced to a quadrature. A condition which ensures that the reciprocal of a solution is also a solution is given, and a first integral to this constraint is found

The impact of the Human Rights Act 1998 on evidence and disclosure in judicial review proceedings

Article assessing the likely impact of the Human Rights Act 1998 on the volume and nature of judicial proceedings in England and Wales including changes in relation to the evidence considered by the court and the growing need for the court to order disclosure. Article by Jonathan Bracken (Partner, Bircham Dyson Bell, London and Scholar in Residence US Law Library of Congress). Published in Amicus Curiae - Journal of the Institute of Advanced Legal Studies and its Society for Advanced Legal Studies. The Journal is produced by the Society for Advanced Legal Studies at the Institute of Advanced Legal Studies, University of London

An Intrinsic Characterization of Bonnet Surfaces Based on a Closed Differential Ideal

The structure equations for a surface are introduced and two required results based on the Codazzi equations are obtained from them. Important theorems pertaining to isometric surfaces are stated and a theorem of Bonnet is obtained. A tranformation formula for the connection forms is developed. It is proved that the angle of deformation must be harmonic. It is shown that the differentials of many of the important variables generate a closed differential ideal. This implies that a coordinate system exists in which many of the variables satisfy particular ordinary differential equations and these results can be used to characterize Bonnet surfaces.Comment: 26 pg

Connections of Zero Curvature and Applications to Nonlinear Partial Differential Equations

A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as well. It is also shown that the connection coefficients can be defined so that the partial differential equation to be studied appears as the curvature term in the structure equations. It is discussed how Lax pairs and Backlund transformations can be formulated for such equations. It is discussed how Lax pairs and Backlund transformations can be formulated for such equations that occur as zero curvature terms.Comment: 2