M-eigenvalues of fourth-order partially symmetric tensors play an important role in many real fields such as quantum entanglement and nonlinear elastic materials analysis. In this paper, we give two bounds for the maximal absolute value of all the M-eigenvalues (called the M-spectral radius) of a fourth-order partially symmetric tensor and discuss the relation of them. A numerical example is gi...

We consider a nonlinear Schrödinger equation in R3 with a bounded local potential. The linear Hamiltonian is assumed to have two bound states with the eigenvalues satisfying some resonance condition. Suppose that the initial data is small and is near some nonlinearexcited state. We give a sufficient condition on the initial data so that the solution to the nonlinear Schrödinger equation approac...

This series of two papers is devoted to the study principal spectral theory nonlocal dispersal operators with almost periodic dependence and asymptotic dynamics nonlinear equations dependence. In first part series, we investigated from aspects: top Lyapunov exponents generalized eigenvalues. Among others, provided various characterizations eigenvalues, established relations between them, studie...

We study uniformly elliptic fully nonlinear equations of the type F (D2u,Du, u, x) = f(x). We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects ; we obtain existence and uniqueness results for non-proper operators whose principal eigenvalues (in some cases, only one of them) are positive ; finally, we obtain an exis...

A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Davey–Stewartson II (DSII) equation. Discrete spectrum in the spectral problem corresponds to eigenvalues embedded into a two-dimensional essential spectrum. We show that these embedded eigenvalues are structurally unstable under small variations of the initial data. This instability...

This work deals with the focusing Nonlinear Schrödinger Equation in one dimension with pure-power nonlinearity near cubic. We consider the spectrum of the linearized operator about the soliton solution. When the nonlinearity is exactly cubic, the linearized operator has resonances at the edges of the essential spectrum. We establish the degenerate bifurcation of these resonances to eigenvalues ...

in this paper, a fundamentally new method, based on the de nition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...

We consider the periodic standing waves in derivative nonlinear Schrodinger (DNLS) equation arising plasma physics. By using a newly developed algebraic method with two eigenvalues, we classify all terms of eight eigenvalues Kaup-Newell spectral problem located at end points bands outside real line. The analytical work is complemented numerical approximation bands, this enables us to fully char...

This dissertation studies solitary waves in collisionally inhomogeneous BoseEinstein condensates in a magnetic trap using a quasi-1D mean-field model. We introduce a model for Bose-Einstein condensate with spatially and temporally modulated nonlinearity. In terms of the spatially periodic nonlinear lattice, we study BECs in a lattice one of which minimum in a period either overlap with the mini...

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least k column vectors, where k is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show t...