Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Zhdanov, R. Z."'
We perform complete group classification of the general class of quasi linear wave equations in two variables. This class may be seen as a broad generalization of the nonlinear d'Alembert, Liouville, sin/sinh-Gordon and Tzitzeica equations. In this w
Externí odkaz:
http://arxiv.org/abs/nlin/0405069
Autor:
Zhdanov, R. Z., Lagno, V. I.
Publikováno v:
Advances in Chemical Physics. Modern Nonlinear Optics, 2001, 119, part II, 269--352
We give the overview of solution techniques for the general conformally-invariant linear and nonlinear wave equations centered around the idea of dimensional reductions by their symmetry groups. The efficiency of these techniques is demonstrated on t
Externí odkaz:
http://arxiv.org/abs/hep-th/0405286
Publikováno v:
J. Math. Phys. 45 (2004), 2280-2313
Group classification of a class of third-order nonlinear evolution equations generalizing KdV and mKdV equations is performed. It is shown that there are two equations admitting simple Lie algebras of dimension three. Next, we prove that there exist
Externí odkaz:
http://arxiv.org/abs/nlin/0201063
Autor:
Zhdanov, R. Z., Lahno, V. I.
We suggest a systematic procedure for classifying partial differential equations invariant with respect to low dimensional Lie algebras. This procedure is a proper synthesis of the infinitesimal Lie's method, technique of equivalence transformations
Externí odkaz:
http://arxiv.org/abs/math-ph/9906003
Autor:
Doebner, H. -D., Zhdanov, R. Z.
The family F of all potentials V(x) for which the Hamiltonian H in one space dimension possesses a high order Lie symmetry is determined. A sub-family F', which contains a class of potentials allowing a realization of so(2,1) as spectrum generating a
Externí odkaz:
http://arxiv.org/abs/math-ph/9809021
Autor:
Zhdanov, R. Z.
Publikováno v:
J.Phys.A30:8761-8770,1997
We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is
Externí odkaz:
http://arxiv.org/abs/hep-th/9708092
Autor:
Zhdanov, R. Z.
Publikováno v:
J.Math.Phys. 37 (1996) 3198-3217
We develop an algebraic approach to studying the spectral properties of the stationary Schr\"odinger equation in one dimension based on its high order conditional symmetries. This approach makes it possible to obtain in explicit form representations
Externí odkaz:
http://arxiv.org/abs/hep-th/9606028
Autor:
Zhdanov, R. Z.
We suggest a generalization of the notion of invariance of a given partial differential equation with respect to Lie-B\"acklund vector field. Such generalization proves to be effective and enables us to construct principally new Ans\"atze reducing ev
Externí odkaz:
http://arxiv.org/abs/solv-int/9505006
Autor:
Zhdanov, R. Z.
Publikováno v:
Quantum Theory & Symmetries - Proceedings of the International Symposium; 2000, p217-220, 4p
Publikováno v:
Journal of Mathematical Physics; Jun2004, Vol. 45 Issue 6, p2280-2313, 34p