ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.11

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The method of one parameter, point symmetric, approximate Lie group invariants is applied to the problem of determining solutions of systems of pure one-dimensional, diffusion equations. The equations are taken to be non-linear in the dependent variables but otherwise homogeneous. Moreover, the matrix of diffusion coefficients is taken to differ from a constant matrix by a linear perturbation with respect to an infinitesimal parameter. The conditions for approximate Lie invariance are developed and are applied to the coupled system. The corresponding prolongation operator is derived and it is shown that this places a power law and logarithmic constraints on the nature of the perturbed diffusion matrix. The method is used to derive an approximate solution of the perturbed diffusion equation corresponding to impulsive boundary conditions.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.12

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

An efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced. The method can be applied to nonintegrable equations as well as to integrable ones. Examples include multisoliton and periodic solutions of the famous integrable evolution equation (KdV) and the new solutions, describing interaction of solitary waves of nonintegrable equation.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.13

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The problem of construction of boundary conditions for nonlinear equations compatible with their higher symmetries is considered. Boundary conditions for the sine-Gordon, Zhiber–Shabat and KdV equations are discussed. New examples are found for the JS equation.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.14

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The singular manifold expansion of Weiss, Tabor and Carnevale [1] has been successfully applied to integrable ordinary and partial differential equations. They yield information such as Lax pairs, Bäcklund transformations, symmetries, recursion operators, pole dynamics, and special solutions. On the other hand, several recent developments have made the application of group theory to the solution of the differential equations more powerful then ever. More recently, Gibbon et. al. [2] revealed interrelations between the Painlevè property and Hirota’s bilinear method. And W. Strampp [3] hase shown that symmetries and recursion operators for an integrable nonlinear partial differential equation can be obtained from the Painlevè expansion. In this paper, it has been shown that the Hirota–Satsuma equation passes the Painlevé test given by Weiss et al. for nonlinear partial differential equations. Furthermore, the data obtained by the truncation technique is used to obtain the symmetries, recursion operators, some analytical solutions of the Hirota–Satsuma equation.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.15

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The different second-order nonlinear partial equations are found that are invariant under the representationof the Poincaré groupP(1, 3) and also under conformal groupC(1, 3). The some exact solutions are constructed for the one of these equations.

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.16

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.17

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.18

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.19

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:1402-9251    

DOI:10.2991/jnmp.1996.3.1-2.20

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor