摘要:

We present a complete proof that solutions of the WDVV equations in Seiberg-Witten theory may be constructed from root systems. A generalization to weight systems is proposed.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.1.1

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

An eigenvalue problem with a reference function and the corresponding hierarchy of nonlinear evolution equations are proposed. The bi–Hamiltonian structure of the hierarchy is established by using the trace identity. The isospectral problem is nonlinearized as to be finite–dimensional completely integrable systems in Liouville sense under Neumann and Bargmann constraints.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.1.2

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The two-dimensional unsteady coupled Burgers’ equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical stability and convergence are presented. Comparisons are made between the present schemes in terms of accuracy and computational efficiency for solving problems with severe internal and boundary gradients. The present study shows that the fourth-order compact ADI scheme is stable and efficient.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.1.3

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics [1]–[6]. In the present paper, using the variational method for solving nonlinear boundary problems of statics of hyper-elastic membranes under the regular hydrostatic load, we investigate peculiarities of deformation of a circular membrane whose mechanical characteristics are described by the Bidermann-type elastic potential. We develop an algorithm for solving a singular perturbation of nonlinear problem for the case of membrane loaded by heavy liquid. This algorithm enables us to obtain approximate solutions both in the presence of boundary layer and without it. The class of admissible functions, on which the variational method is realized, is chosen with account of the structure of formal asymptotic expansion of solutions of the corresponding linearized equations that have singularities in a small parameter at higher derivatives and in the independent variable. We give examples of calculations that illustrate possibilities of the method suggested for solving the problem under consideration.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.1.4

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Symmetry classification of two-body central potentials in a two-particle Schrödinger equation in terms of contact transformations of the equation has been investigated. Explicit calculation has shown that they are of the same four different classes as for the point transformations. Thus in this problem contact transformations are not essentially different from point transformations. We have also obtained the detailed algebraic structures of the corresponding Lie algebras and the functional bases of invariants for the transformation groups in all the four classes.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.1.5

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.1.6

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditionsψ(x1, 0)ψ†(x2, t)±,T. We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special casex1= 0, we express correlation functions with Neumann boundary conditionsψ(0, 0)ψ†(x2, t)+,T, in terms of solutions of nonlinear partial differential equations which were introduced in [1] as a generalization of the nonlinear Schrödinger equations. We generalize the Fredholm minor determinant formulae of ground state correlation functionsψ(x1)ψ†(x2)±,0in [2], to the Fredholm determinant formulae for the time and temperature dependent correlation functionsψ(x1, 0)ψ†(x2, t)±,T,t ∈R,T ≥0.

ISSN:1402-9251    

DOI:10.2991/jnmp.1999.6.1.7

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor