相关论文: Block-diagonalization of the linearized coupled-mo…

In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form…

Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…

A coupled pair of waveguides with refractive indices of different signs is considered. It is shown that the gap in the linear wave spectrum closes if these waves are amplitude modulated. To look for solitons as envelopes of exponentially…

General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…

In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical…

In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…

We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find…

We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…

We present a complete analytical solution for a single four-level atom strongly coupled to a cavity field mode and driven by external coherent laser fields. The four-level atomic system consists of a three-level subsystem in an EIT…

We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of…

The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…

We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the…

We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…

By using of an appropriate transformation, it was shown that the quantum system of 4 dimensional simple harmonic oscillator can describe the motion of a charged particle in the presence of a magnetic monopole field. It was shown that the…

We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase shift between them, in a medium with the uniform Kerr…

A sequence of representations \(V_n\) of the symmetric group \(S_n\) is called representation (multiplicity) stable if, after some \(n\), the irreducible decomposition of \(V_n\) stabilizes. In particular, Church, Ellenburg and Farb (2015)…

The coupling of the high-lying dipole mode to the low-lying quadrupole modes for the case of deformed gamma-unstable nuclei is studied. Results from the geometrical model are compared to those obtained within the dipole boson model.…

We study, both theoretically and experimentally, the scattering properties of optical dipole-mode vector solitons - radially asymmetric composite self-trapped optical beams. First, we analyze the soliton collisions in an isotropic…

We study the existence and stability of solitons in the quadratic nonlinear media with spatially localized ${\cal PT}$-symmetric modulation of the linear refractive index. Families of stable one and two hump solitons are found. The…

This work models the propagation of an optical pulse in a 4-level atomic system in the electromagnetic induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a…