摘要:

A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlevé; test for integrability well, and its 4×4 Lax pair with two spectral parameters is found. The results show that the Painlevé; classification of coupled KdV equations by A. Karasu should be revised.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.3.1

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as local symmetries of a related auxiliary system, are obtained. For some special nonlinearities new symmetry reductions and exact solutions are derived by using the nonclassical method.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.3.2

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Dedicated with gratitude to my teacher, Alexander Mikhailovich Vinogradov, on occasion of his 60thanniversary.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.3.3

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (“acceleration equal force”) equations of motion, featuring one-body (“external”) and pair (“interparticle”) forces. The former depend quadratically on the velocity, and nonlinearly on the coordinate, of the moving particle. The latter depend linearly on the coordinate of the moving particle, and linearly respectively nonlinearly on the velocity respectively the coordinate of the other particle. The model contains 2n2arbitrary coupling constants,nbeing the number of particles. The behaviour of the solutions is outlined; special cases in which the motion is confined (multiply periodic), or even completely periodic, are identified.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.3.4

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Expanded version of a talk presented at the Special Session on ‘Octonions and Clifford Algebras’, 1997 Spring Western Sectional 921st Meeting of the American Mathematical Society, Oregon State University, Corvallis, OR, 19–20 April 1997.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.3.5

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The concept of the theory of continuous groups of transformations has attracted the attention of applied mathematicians and engineers to solve many physical problems in the engineering sciences. Three applications are presented in this paper. The first one is the problem of time-dependent vertical temperature distribution in a stagnant lake. Two cases have been considered for the forms of the water parameters, namely water density and thermal conductivity. The second application is the unsteady freeconvective boundary-layer flow on a non-isothermal vertical flat plate. The third application is the study of the dispersion of gaseous pollutants in the presence of a temperature inversion. The results are found in closed form and the effect of parameters are discussed.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.3.6

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form−div (a(x, x/εh, Duh)) =fhon Ω with Dirichlet boundary conditions. The sequence (εh) tends to 0 and the mapa(x, y, ξ) is periodic iny, monotone inξand satisfies suitable continuity conditions. It is proved thatuh→ uweakly inwhereuis the solution of a homogenized problem−div(b(x, Du)) =fon Ω. We also prove some corrector results, i.e. we find (Ph) such thatDuh− Ph(Du)→0 inL2(Ω, Rn).

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.3.7

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor