In this paper, we study the initial value problem for focusing nonlinear Schrödinger (fNLS) equation with non-generic weighted Sobolev data that allows presence of high-order discrete spectrum. More precisely, show how to characterize properties eigenfunctions and scattering coefficients in poles; Further is formulated into an appropriate enlarged RH problem, which transformed a solvable model ...

A continuum medium approach is proposed to describe the finite size dependent effects for the 1D isotropic Heisenberg ferromagnet. The results are compared to the exact Bethe ansatz solution for the finite chain. The approach is shown to adequately account for the behaviour of the eigenfunctions and eigenenergies. The continuum is obtained by integration in Fourier space via introduction of cut...

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In this note we present some constructions with generators of analytic semigroups which are an abstract version of the familiar method of “freezing the coefficients” to prove elliptic estimates for differential operators with continuous coefficients or Hölder-continuous coefficients. As a side result we obtain an abstract exponential decay result for, say eigenfunctions corresponding to isolate...

We give necessary and sufficient conditions to have measurable and continuous eigenfunctions for linearly recurrent Cantor dynamical systems. We also construct explicitly an example of linearly recurrent system with nontrivial Kronecker factor and a trivial maximal equicontinuous factor.

The paper investigates the possibility for giving a general definition of the fractional Fourier transform (FRT) for all signal classes [one-dimensional (1-D) and multidimensional, continuous and discrete, periodic and aperiodic]. Since the definition is based on the eigenfunctions of the ordinary Fourier transform (FT), the preliminary conditions is that the signal domain/periodicity be the sa...

where L is a symmetric elliptic operator and r is a locally integrable function on Rn. If r is of constant sign then this problem leads to a selfadjoint problem in the Hilbert space L2(|r|). In this note we are interested in the case when r takes both positive and negative values on sets of positive measure. Then the spectrum of the problem (1) is not necessarily real any more. Moreover it is n...

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

A technique for analyzing dispersion properties of numerical schemes is proposed. The method is able to deal with both non dispersive or dispersive waves, i.e. waves for which the phase speed varies with wavenumber. It can be applied to unstructured grids and to finite domains with or without periodic boundary conditions. We consider the discrete version L of a linear differential operator L. A...

33]. algebraic [5]. Angular [24]. Applications [30]. arbitrary [8]. associated [18]. Axiomatic [31]. between [27]. bounded [11, 14]. Boundedness [16]. Cayleyan [4]. certain [9]. characteristic [35]. combinatorial [30]. Completely [13]. Congruence [27]. conjugate [7]. continuous [12]. convex [7]. courbure [2]. critical [8]. curvature [24, 2]. degree [33, 11]. density [25]. differential [18]. dim...