We study the effect of lifting the degeneracy of vortex modes with a parity time (PT) symmetric defect, using discrete vortices in a circular array of nonlinear waveguides as an example. When the defect is introduced, the degenerate linear vortex modes spontaneously break PT symmetry and acquire complex eigenvalues, but nonlinear propagating modes with real propagation constants can still exist...

By considering a constraint on the energy profile, a new implicit approach is developed to solve nonlinear eigensolution problems. A corresponding minimax method is modified to numerically find eigensolutions in the order of their eigenvalues to a class of semilinear elliptic eigensolution problems from nonlinear optics and other nonlinear dispersive/diffusion systems. It turns out that the con...

In 11 ] the Reduction to Scalar CDS method for the solution of separably stiff initial value problems is proposed. In this paper an improved version is given that is equivalent for linear problems but considerably superior for nonlinear problems. A naturally arising numerical example is given, for which the old version fails, yet the new version yields very good results. The disadvantage of the...

This paper is concerned with the reconstruction of an unknown impedance p(x) in the Sturm-Liouville problem with Dirichlet boundary conditions, when only a nite number of eigenvalues are known. The problem is transformed into a system of nonlinear equations. A solution of this system is enclosed in an interval vector by an interval Newton's method. From the interval vector, an interval function...

Linear stability of multi-vector-soliton bound states in the coupled nonlinear Schrodinger equations is analyzed using a new tailmatching method. Under the condition that individual vector solitons in the bound states are wave-and-daughter-waves and widely separated, small eigenvalues of these bound states that bifurcate from the zero eigenvalue of single vector solitons are calculated explicit...

In this paper we study the dependence of the Lidstone eigenvalues λm(q) , m ∈ N , of the fourth-order beam equation on potentials q ∈ Lp[0,1] , 1 p ∞ . The first result is that λm(q) have a strongly continuous dependence on potentials, i.e., as nonlinear functionals, λm(q) are continuous in q ∈ Lp[0,1] when the weak topology is considered. The second result is that λm(q) are continuously Fréche...

We obtain the most general matrix criterion for stability and instability of multicomponent solitary waves by considering a system of N incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained variational problem which is reduced to finite-dimensional linear algebra. We prove that unstable (all real and positive) eigenvalues of the linear stability pro...

In this paper, the solution expansion for an inverted pendulum system with time delay is studied. The linearized model of this nonlinear system near its equilibrium is derived on the assumption that a unique equilibrium exists in it. Then the asymptotic expressions of its eigenvalues and the eigenvalues’ corresponding eigenvectors are obtained. Moreover, although the set of these eigenvectors d...