摘要:

A comprehensive application is presented of a recent theory concerning a geometric characterization of separable second-order differential equations. The main purpose of the paper is to illustrate how the practical algorithm developed from this theory effectively works, and what the significance is of the different conditions entering the separability theorem. These conditions are recalled in a coordinate representation, so as to make the paper sufficiently self-contained for practical computations.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.1.1

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Three third-order differential equations are obtained for the canonical system. These equations are equivalent to the initial system and characterize its components. The first equation is Lipschitz continuous, the second one has discontinuous right hand side and the third one is an equation with impulse action. The equation in variations which corresponds to solutions of the first equation is investigated; analysis of its solutions is given; conditions for presence of periodic solutions for Chua’s system are discussed. The canonical form for the general system of Chua’s type is obtained.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.1.2

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We calculate symmetries of the nonlinearn-dimensional wave equation and its approximations. In particular, we study the conformal invariance of the equations. Conditional symmetries of the approximate system are also considered whereby approximate solutions are constructed.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.1.3

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We construct a number of ansatzes that reduce one-dimensional nonlinear heat equations to systems of ordinary differential equations. Integrating these, we obtain new exact solution of nonlinear heat equations with various nonlinearities.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.1.4

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

By use of nonlinearization method about spectral problem, a classical completely integrable system associated with the Harry-Dym (HD) hierarchy is obtained. Furthermore, the involutive solution of each equation in theHDhierarchy is presented, in particular, the involutive solution of the well-knownHDequationis given.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.1.5

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes equations are constructed.

ISSN:1402-9251    

DOI:10.2991/jnmp.1994.1.1.6

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor