摘要:

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.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.1.1

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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 functionsf(u) for which this equation admit either the classical or the nonclassical method. The reductions obtained are derived. Some new exact solutions can be derived.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.1.2

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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 investigate symmetry properties of the equation with convection term. The contact transformations of the Schrödinger equation with potential are obtained.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.1.3

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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 impose some regularity assumptions over the kernels of the differential forms. This allows us to define an exterior stochastic differential derivative over these forms.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.1.4

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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 derived equations are solved by using a nonlinear perturbation method. The dependence of the interfacial profile on the triangular obstacle size, as well as its dependence on some flow parameters, such as the ratios of depths and densities of the two fluids, have been studied.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.1.5

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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 on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.1.6

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

We investigate Lie symmetries of Einstein’s vacuum equations inNdimensions, 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 of all independent partial derivatives (which involves a very complicated substitution of Einstein’s equations), we set to zero the coefficients of derivatives that do not appear in Einstein’s equations. This considerably constrains the coefficients of symmetry generating vector fields. Using the Lie algebra property of generators of symmetries and the fact that general coordinate transformations are symmetries of Einstein’s equations, we are then able to obtain all the Lie symmetries. The method we have used can likely be applied to other types of equations.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.1.7

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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, Bäcklund or Darboux Transformations as well asτ-functions, in a unified way. Besides to present the basics of the Method we exemplify this approach by applying it to four equations in (1+1)-dimensions. Two of them are related with the other two through Miura transformations that are also derived by using the Singular Manifold Method.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.1.8

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor