In a recent paper Sima, Van Huffel and Golub [Regularized total least squares based on quadratic eigenvalue problem solvers. BIT Numerical Mathematics 44, 793 812 (2004)] suggested a computational approach for solving regularized total least squares problems via a sequence of quadratic eigenvalue problems. Taking advantage of a variational characterization of real eigenvalues of nonlinear eigen...

In this paper, a new method for finding a state feedback matrix in order to control simultaneously a collection of linear systems (of the same size) by using similarity operations is presented. For stabilization of all the systems, it is necessary that the eigenvalues of the closed-loop systems lie inside a specified region in the left hand side of the complex plane. This aim is achieved by sol...

In this paper we consider solutions of a nonlinear Schrodinger equation with a parabolic and a periodic potential motivated from the dynamics of Bose-Einstein condensates. Our starting point is the corresponding linear problem which we analyze through regular perturbation and homogenization techniques. We then use Lyapunov-Schmidt theory to establish the persistence and bifurcation of the linea...

In this article we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter l. This nonlinear dependence on l is allowed both in the leading coefficient and in the potential. We extend the traditional notions of eigenvalues and eigenfunctions to this more general setting. Our main result generalizes the re...

With the aim of exploring a massive model corresponding to the perturbation of the conformal model [1] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is derived from an integrable lattice field theory. The eigenvalues of the energy and of the transfer matrix (and of all the other local integrals of motion) are expressed in...

We consider a linear Schrödinger equation with a small nonlinear perturbation in R3. Assume that the linear Hamiltonian has exactly two bound states and its eigenvalues satisfy some resonance condition. We prove that if the initial data is near a nonlinear ground state, then the solution approaches to certain nonlinear ground state as the time tends to infinity. Furthermore, the difference betw...

This paper proposes some nonlinear Uzawa methods for solving linear and nonlinear saddle-point problems. A nonlinear inexact Uzawa algorithm is first introduced for linear saddlepoint problems. Two different PCG techniques are allowed in the inner and outer iterations of the algorithm. This algorithm is then extended for a class of nonlinear saddle-point problems arising from some convex optimi...

The synchronization of nonlinear systems connected over large-scale networks has gained popularity in a variety of applications, such as power grids, sensor networks, and biology. Stochastic uncertainty in the interconnections is a ubiquitous phenomenon observed in these physical and biological networks. We provide a size-independent network sufficient condition for the synchronization of scala...

In the present work we examine both the linear and nonlinear properties of two related parity-time (PT)-symmetric systems of the discrete nonlinear Schrödinger (dNLS) type. First, we examine the parameter range for which the finite PT-dNLS chains have real eigenvalues and PT-symmetric linear eigenstates. We develop a systematic way of analyzing the nonlinear stationary states with the implicit ...

An efficient technique is presented for optimum design of structures with both natural frequency and complex frequency response constraints. The main ideals to reduce the number of dynamic analysis by introducing high quality approximation. Eigenvalues are approximated using the Rayleigh quotient. Eigenvectors are also approximated for the evaluation of eigenvalues and frequency responses. A tw...