Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 3, Issue 3-4, September 1996
Jarmo HIETARINTA
Pages: 260 - 265
One of the most powerful methods for finding and solving integrable nonlinear partial differential equations is Hirota's bilinear method. The idea behind it is to make first a nonlinear change in the dependent variables after which multisoliton solutions of integrable systems can be expressed as polynomials...
Peter BASARAB-HORWATH
Pages: 311 - 318
We give ansatzes obtained from Lie symmetries of some hyperbolic equations which reduce these equations to the heat or Schrödinger equations. This enables us to construct new solutions of the hyperbolic equations using the Lie and conditional symmetries of the parabolic equations. Moreover, we note...
Vladimir F. KOVALEV
Pages: 351 - 356
Results of renormgroup analysis of a quasi-Chaplygin system of equations are presented. Lie-Bäcklund symmetries and corresponding invariant solutions for different "Chaplygin" functions are obtained. The algorithm of construction of a group on a solution (renormgroup) using two different approaches...
S.P. ONUFRIICHUK, O.I. PRYLYPKO
Pages: 385 - 387
We study hidden symmetry of a two-particle system of equations for parastates. Invariance operators are described for various potentials. It is a well-known fact that the systems of partial differential equations have a hidden symmetry, which can not be observed in the classical approach of Lie [1].
S.P. ONUFRIICHUK, O.I. PRYLYPKO
Pages: 388 - 390
In this paper we find the complete set of symmetry operators for the two-particle Breit equation in the class of first-order differential operators with matrix coefficients. A new integral of motion is obtained.
G.A. KOTELNIKOV
Pages: 391 - 395
The infinite series of Lorentz and Poincaré-invariant nonlinear versions of the Maxwell equations are suggested. Some properties of these equations are considered.
Olena ROMAN
Pages: 435 - 440
We present symmetry classification of the polywave equation 2l u = F(u). It is established that the equation in question is invariant under the conformal group C(1, n) iff F(u) = eu , n + 1 = 2l or F(u) = u(n+1+2l)/(n+1-2l) , n + 1 = 2l. Symmetry reduction for the biwave equation 22 u = uk is carried...
A.A. BORGHARDT, D.Ya. KARPENKO, N.Yu. NOSENKO
Pages: 458 - 463
Fundamental solutions (FS) with a given boundary condition on the characteristics of relativistic problems with axial symmetry are considered. This is so-called the Goursat problem (GP) or zero plane formalism in Dirac's terminology, or modification of the proper time method in the Fock-Nambu-Schwinger...
Ivan FEDORCHUK
Pages: 474 - 477
By means of splitting subgroups of the generalized Poincaré group P(1, 4), ansatzes which reduce the eikonal equation to differential equations with fewer independent variables have been constructed. The corresponding symmetry reduction has been done. By means of the solutions of the reduced equations...