
On the question of extended twodimensional nonrelativistic supersymmetry
An algorithm for realizing the algebra of twodimensional supersymmetric quantum mechanics is described. The cases N = 2 and N = 3 are described in detail. The procedure for iterating Darboux transformations is considered separately. In contrast to the onedimensional case, in which the problem is completely solved by Krum's formulas, iterations of twodimensional Darboux transformations remain insufficiently understood.
Yurova A. A., Chirikov R. V.
supersymmetry, Darboux transform, 2DHamiltonian...

Twodimensional supersymmetric quantum mechanics and the Moutard transformations
This is a treatise on a twodimensional supersymmetric hamiltonian H whose components consists of two scalar (h0, h1) and one matrixvalued hml quantummechanical Hamiltonians with constant terms added to the mix. In particular, the article discusses the ways to utilize a known solution of the spectral problem for operator h0 in the multidimensional generalization of the factorization method in order to produce such hml and h1 that their groundstate eigenvalues will be identical to each...

New classes of exact solutions and consistent models of cosmological evolution
A method for construction of exact cosmological solutions of Einstein equations is developed. The method is based on representation of these equations as a secondorder linear differential equation. Particularly, the method allows to construct a more general solution, parametrized by two constants, using any known solution. Also it is shown, that in a specific case new classes of exact solutions have singularities with the following property: a geodesic, which begins or ends in the singularity, has...