Journal of Nonlinear Mathematical Physics
Volume 6, Issue 1, February 1999
R. Martini, P.K.H. Gragert
Pages: 1 - 4
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.
Pages: 5 - 12
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...
3. On the Fourth-Order Accurate Compact ADI Scheme for Solving the Unsteady Nonlinear Coupled Burgers' Equations
Samir F. Radwan
Pages: 13 - 34
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...
4. Variational Methods for Solving Nonlinear Boundary Problems of Statics of Hyper-Elastic Membranes
Pages: 35 - 50
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics . In the present paper, using the variational method for solving nonlinear boundary problems of statics of hyper-elastic membranes under the regular...
5. Contact Symmetry of Time-Dependent Schrödinger Equation for a Two-Particle System: Symmetry Classification of Two-Body Central Potentials
Pages: 51 - 65
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...
Peter A. Clarkson, Thomas J. Priestley
Pages: 66 - 98
In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations utt = u + u2 xx + uuxxxx + µuxxtt + uxuxxx + u2 xx, (1) where , , , and µ are arbitrary constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm...
7. Dynamical Correlation Functions for an Impenetrable Bose Gas with Neumann or Dirichlet Boundary Conditions
Pages: 99 - 119
We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions (x1, 0) (x2, t) ±,T . We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case x1 = 0, we express...