From a theory developed by C. Mehl, et al., a theory of the rank one perturbation of Hamiltonian systems with periodic coefficients is proposed. It is shown that the rank one perturbation of the fundamental solution of Hamiltonian system with periodic coefficients is solution of its rank one perturbation. Some results on the consequences of the strong stability of these types of systems on thei...

An efficient Singular Value Decomposition (SVD) algorithm is an important tool for distributed and streaming computation in big data problems. It is observed that update of singular vectors of a rank-1 perturbed matrix is similar to a Cauchy matrix-vector product. With this observation, in this paper, we present an efficient method for updating Singular Value Decomposition of rank1 perturbed ma...

We study analytic behavior of eigenvalues the generalized Friedrichs model $$H_\mu (p)$$ , with a rank-one perturbation, depending on parameters $$\mu >0$$ and $$p\in {\mathbb {T}}^2$$ . Under certain conditions, existence unique eigenvalue lying below essential spectrum has been shown in Lakaev (Abstract Appl Anal 2012, 2012). Here, we obtain an absolutely convergent expansion for that at coup...

We develop a perturbation theory for bright solitons of the F=1 integrable spinor Bose-Einstein condensates BEC model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution of the soliton parameters. Both rank-one and rank-two soliton solutions of the model are obtained. We prove equivalence of the rank-one soliton and the ferroma...