Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 2, Issue 3-4, September 1995
Pages: 216 - 235
In this talk I am going to present a brief review of some key ideas and methods which were given start and were developed in Kyiv, at the Institute of Mathematics of National Academy of Sciences of Ukraine during recent years.
Pages: 236 - 246
The Program SUBMODELS [1] is aimed to exhaust all possibilities derived from the symmetry of differential equations for construction of submodels (i.e., systems of equations of the reduced dimension) which describe classes of exact solutions for initial equations. In the frame of this Program, our...
Pantelis A. DAMIANOU, Paschalis G. PASCHALI
Pages: 269 - 277
We study symmetries of the real Maxwell-Bloch equations. We give a Lax pair, biHamiltonian formulations and we find a symplectic realization of the system. We have also constructed a hierarchy of master symmetries which is used to generate nonlinear Poisson brackets. In addition we have calculated...
Pages: 312 - 318
Operators of nonlocal symmetry are used to construct exact solutions of nonlinear heat equations In [1] the idea of constructing nonlocal symmetry of differential equations was proposed. By using this symmetry, we have suggested a method for finding new classes of ansatzes reducing nonlinear wave...
Pages: 356 - 366
Consider the operator pencil L = A - B - 2 C, where A, B, and C are linear, in general unbounded and nonsymmetric, operators densely defined in a Hilbert space H. Sufficient conditions for the existence of the eigenvalues of L are investigated in the case when A, B and C are K-positive and K-symmetric...
Anatolii NIKITIN
Pages: 405 - 415
Appeared more than one century ago, the classical Lie approach serves as a powerful tool in investigations of symmetries of partial differential equations. In the last three decades there appear essential generalizations of this approach. They are the modern version of the Lie-Bäcklund symmetries...