摘要:

As an example of how to deal with nonintegrable systems, the nonlinear partial differential equation which describes the evolution of long surface waves in a convecting fluidis fully analyzed, including symmetries (nonclassical and contact transformatons), similarity reductions and the application of the ARS algorithm to the reductions. As a result of the calculations, the Galilean invariance of the equation is shown and all the possible solutions arising from the related ODE through these methods are obtained and classified in terms of the physical parameters.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.1

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The Lie point symmetries associated with a number of (2 + 1)-dimensional generalizations of soliton equations are investigated. These include the Niznik – Novikov – Veselov equation and the breaking soliton equation, which are symmetric and asymmetric generalizations respectively of the KDV equation, the (2+1)-dimensional generalization of the nonlinear Schrödinger equation by Fokas as well as the (2+1)-dimensional generalized sine-Gordon equation of Konopelchenko and Rogers. We show that in all these cases the Lie symmetry algebra is infinite-dimensional; however, in the case of the breaking soliton equation they do not possess a centerless Virasorotype subalgebra as in the case of other typical integrable (2+1)-dimensional evolution equations. We work out the similarity variables and special similarity reductions and investigate them.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.2

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.3

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A brief review is presented of the two recent perturbation algorithms. Their common idea lies in a not quite usual treatment oflinearSchrödinger equations vianonlinearmathematical means.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.4

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.5

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.6

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Computer-aided symbolic and graphic computation allows to make significantly easier both theoretical and applied symmetry analysis of PDE. This idea is illustrated by applying a special “Mathematica” package for obtaining conditional symmetries of the nonlinear wave equationut= (u ux)xinvariant or partially invariant under its classical Lie symmetries.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.7

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We search for hidden symmetries of two-particle equations with oscillator-equivalent potential proposed by Moshinsky with collaborators. We proved that these equations admit hidden symmetries and parasupersymmetries which enable easily to find the Hamiltonian spectra using algebraic methods.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.8

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Properties of approximate symmetries of equations with a small parameter are discussed. It turns out that approximate symmetries form an approximate Lie algebra. A concept of approximate invariants is introduced and the algorithm of their calculating is proposed.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.9

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.10

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor