arXiv subjects

V. G. Makhankov

Publications and source records attributed to V. G. Makhankov.

3 recordsLinked to original sources

arXiv2016

Gauge Equivalence, Supersymmetry and Classical Solutions of the ospu($1, 1/1$) Heisenberg Model and the Nonlinear Schrödinger Equation

An integrable generalization of the continuous classical O$(2,1)$ pseudospin Heisenberg model to the case of the ospu$(1,1/1)$ superalgebra is constructed. The gauge equivalence of the constructed model and the related NLSE is established. We indicate a method of generating classical solutions using the global ospu$(1,1/1)$ supersymmetry. The relationship between solutions of O$(2,1)$ HM and 'superpartners' of NLSE is obtained.

nlin.SI↗

arXiv1996

Generalized Coherent States and Spin $S\geq 1$ Systems

Generalized Coherent States (GCS) are constructed (and discussed) in order to study quasiclassical behaviour of quantum spin models of the Heisenberg type. Several such models are taken to their semiclassical limits, whose form depends on the spin value as well as the Hamiltonian symmetry. In the continuum approximation, SU(2)/U(1) GCS when applied give rise to the well-known Landau-Lifshitz classical phenomenology. For arbitrary spin values one obtains a lattice of coupled nonlinear oscillators. Corresponding classical continuum models are described as well.

chao-dyn↗

arXiv1993

On exact solution for some integrable nonlinear equations of the Schrödinger type

The outlook of a simple method to generate localized (soliton-like) potentials of time-dependent Schrodinger type equations is given. The conditions are discussed for the potentials to be real and nonsingular. For the derivative Schrodinger equation also is discussed its relation to the Ishimori-II model. Some pecular soliton solutions of nonlinear Schrodinger type equations are given and discussed.

solv-int↗