Journal of Nonlinear Mathematical Physics

Volume 2, Issue 2, May 1995

2. (p, q)-Analog of Two-Dimensional Conformal Field Theory. The Ward Identities and Correlation Functions

I.M. BURBAN
Pages: 114 - 119
A (p, q)-analog of two-dimensional conformally invariant field theory based on the quantum algebra Upq(su(1, 1)) is proposed. The representation of the algebra Upq(su(1, 1)) on the space of quasi-primary fields is given. The (p, q)-deformed Ward identities of conformal field theory are defined. The two-...

4. Representations of -algebras and dynamical systems

Vasyl' L. OSTROVSKYI, Yurii S. SAMOILENKO
Pages: 133 - 150
Consider a -algebra A generated by self-adjoint elements a1, . . . , an (aj = a j , j = 1, . . . , n) and the relations Pk(a1, . . . , an) = 0 (k = 1, . . . , m). (1) Here Pk(·) are polynomials in the non-commuting variables a1, . . . , an over C such that P k (·) = Pk(·). In other words, A is a quotient...

5. Commutator representations of nonlinear evolution equations: Harry-Dym and Kaup-Newell cases

Zhijun QIAO
Pages: 151 - 157
A general structure of commutator representations for the hierarchy of nonlinear evolution equations (NLEEs) is proposed. As two concrete examples, the Harry-Dym and Kaup-Newell cases are discused.

6. Internal Gravity Waves with Free Upper Surface Over an Obstacle

M.B. ABD-EL-MALEK, A.H. TEWFICK
Pages: 158 - 171
In this paper we discuss a theoretical model for both the free-surface and interfacial profiles of progressive nonlinear waves which result from introducing an obstacle of finite height, in the form of a ramp of gentle slope, attached to the bottom below the flow of a stratified, ideal, two-layer fluid....

7. On non-Lie ansatzes and new exact solutions of the classical Yang-Mills equations

Renat ZHDANOV, Wilhelm FUSHCHYCH
Pages: 172 - 181
We ssuggest an effective method for reducing Yang-Mills equations to systems of ordinary differential equations. With the use of this method, we construct wide families of new exact solutions of the Yang-Mills equations. Analysis of the solutions obtained shows that they correspond to conditional symmetry...

8. Elliptic even finite-gap potentials and spectra of the Schrödinger operator

A.M. KOROSTIL'
Pages: 182 - 192
A simple method for calculating finite-gap elliptic potentials and corresponding spectra of the one-dimensional Schrödinger operator which is based on a general representation of the potentials in a form of rational functions of the Weierstrass function and trace formulae is proposed. It is shown that...