Communications in Theoretical Physics, ISSN 0253-6102, 09/2017, Volume 68, Issue 3, pp. 301 - 308

Journal Article

2.
A Weyl-Titchmarsh type formula for a discrete Schrödinger operator with Wigner-von Neumann potential

Studia Mathematica, ISSN 0039-3223, 2010, Volume 201, Issue 2, pp. 167 - 189

We consider a discrete Schrodinger operator J with Wigner-von Neumann potential not belonging to l(2). We find the asymptotics of orthonormal polynomials...

Discrete schrö | Dinger operator | Asymptotics of generalized eigenvectors | Orthogonal polynomials | Jacobi matrices | Weyl-Titchmarsh theory | Wigner-von neumann potential | LINEAR-SYSTEMS | PERTURBATIONS | SUBORDINACY | discrete Schrodinger operator | ABSOLUTE CONTINUITY | MATHEMATICS | JOST FUNCTIONS | THEOREMS | asymptotics of generalized eigenvectors | INVERSE SCATTERING PROBLEM | HAMILTONIANS | ASYMPTOTICS | Wigner-von Neumann potential | orthogonal polynomials

Discrete schrö | Dinger operator | Asymptotics of generalized eigenvectors | Orthogonal polynomials | Jacobi matrices | Weyl-Titchmarsh theory | Wigner-von neumann potential | LINEAR-SYSTEMS | PERTURBATIONS | SUBORDINACY | discrete Schrodinger operator | ABSOLUTE CONTINUITY | MATHEMATICS | JOST FUNCTIONS | THEOREMS | asymptotics of generalized eigenvectors | INVERSE SCATTERING PROBLEM | HAMILTONIANS | ASYMPTOTICS | Wigner-von Neumann potential | orthogonal polynomials

Journal Article

3.
Full Text
Localized modes in two-dimensional Schro¨dinger lattices with a pair of nonlinear sites

Optics Communications, ISSN 0030-4018, 08/2014, Volume 324, pp. 277 - 285

We address the existence and stability of localized modes in the two-dimensional (2D) linear Schrödinger lattice with two symmetric nonlinear sites embedded...

Localized nonlinearity | 2D discrete solitons | Spontaneous symmetry breaking | Broken symmetry | Stability | Asymmetry | Lattices | Nonlinearity | Schroedinger equation | Two dimensional | Lattice vibration

Localized nonlinearity | 2D discrete solitons | Spontaneous symmetry breaking | Broken symmetry | Stability | Asymmetry | Lattices | Nonlinearity | Schroedinger equation | Two dimensional | Lattice vibration

Journal Article

Izvestiya Mathematics, ISSN 1064-5632, 2012, Volume 76, Issue 5, pp. 946 - 966

We consider a family of discrete Schrodinger operators H-mu(k), k is an element of & subset of T-d. These operators are associated with the Hamiltonian H-mu of...

Eigenvalue | Hamiltonian system of two particles | Zero-range (contact) potential | Dinger operator | Asymptotic behaviour | Discrete Schrö | MATHEMATICS | BOUND-STATES | TRANSFER-MATRICES | GIBBS FIELDS | discrete Schrodinger operator | asymptotic behaviour | SPECTRUM | RESONANCES | zero-range (contact) potential | eigenvalue

Eigenvalue | Hamiltonian system of two particles | Zero-range (contact) potential | Dinger operator | Asymptotic behaviour | Discrete Schrö | MATHEMATICS | BOUND-STATES | TRANSFER-MATRICES | GIBBS FIELDS | discrete Schrodinger operator | asymptotic behaviour | SPECTRUM | RESONANCES | zero-range (contact) potential | eigenvalue

Journal Article

Physics Letters A, ISSN 0375-9601, 08/2014, Volume 378, Issue 38-39, pp. 2824 - 2830

We consider a PT-symmetric chain (ladder-shaped) system governed by the discrete nonlinear Schrödinger equation where the cubic nonlinearity is carried solely...

Discrete nonlinear Schrödinger equation | Cubic nonlinearity | [formula omitted]-symmetry | PT-symmetry | Discrete nonlinear Schro¨dinger equation | PHYSICS, MULTIDISCIPLINARY | NONLINEAR IMPURITIES | STATIONARY LOCALIZED STATES | Discrete nonlinear Schrodinger equation | Electrical engineering | Analysis

Discrete nonlinear Schrödinger equation | Cubic nonlinearity | [formula omitted]-symmetry | PT-symmetry | Discrete nonlinear Schro¨dinger equation | PHYSICS, MULTIDISCIPLINARY | NONLINEAR IMPURITIES | STATIONARY LOCALIZED STATES | Discrete nonlinear Schrodinger equation | Electrical engineering | Analysis

Journal Article

Russian Journal of Mathematical Physics, ISSN 1061-9208, 07/2003, Volume 10, Issue 3, pp. 296 - 318

Our aim is the study of multidimensional difference operators Au(x) = Sigma(\alpha\less than or equal tom) a(alpha)(x)V(alpha)u(x), x is an element of Z(n),...

Eigenfunctions of discrete schrö | Dinger operators | PHYSICS, MATHEMATICAL | BAND-DOMINATED OPERATORS

Eigenfunctions of discrete schrö | Dinger operators | PHYSICS, MATHEMATICAL | BAND-DOMINATED OPERATORS

Journal Article

2000, ISBN 0471805416, xii, 361

Book

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2011, Volume 33, Issue 2, pp. 1008 - 1033

This paper addresses the construction of different families of absorbing boundary conditions for the one- and two-dimensional Schrodinger equations with a...

Relaxation scheme | Fixed point algorithm | Pseudodifferential operators | Stable semidiscrete schemes | Absorbing boundary conditions | Nonlinear Schrödinger equation with potential | absorbing boundary conditions | stable semidiscrete schemes | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | fixed point algorithm | pseudodifferential operators | nonlinear Schrodinger equation with potential | PERFECTLY MATCHED LAYER | relaxation scheme | SCHEMES | Studies | Nonlinear equations | Accuracy | Schrodinger equation | Efficiency | Numerical Analysis | Mathematics | General Mathematics

Relaxation scheme | Fixed point algorithm | Pseudodifferential operators | Stable semidiscrete schemes | Absorbing boundary conditions | Nonlinear Schrödinger equation with potential | absorbing boundary conditions | stable semidiscrete schemes | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | fixed point algorithm | pseudodifferential operators | nonlinear Schrodinger equation with potential | PERFECTLY MATCHED LAYER | relaxation scheme | SCHEMES | Studies | Nonlinear equations | Accuracy | Schrodinger equation | Efficiency | Numerical Analysis | Mathematics | General Mathematics

Journal Article

10.
Full Text
N-bright-dark soliton solution to a semi-discrete vector nonlinear Schrödinger equation

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 09/2017, Volume 13

In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirota's...

Hirota’s bilinear method | Semi-discrete vector NLS equation | Bright-dark soliton | Pfaffian | semi-discrete vector NLS equation | Hirota's bilinear method | INVERSE SCATTERING TRANSFORM | PHYSICS, MATHEMATICAL | OPTICAL PULSES | bright-dark soliton | DISCRETIZATION | TRANSMISSION | WAVES | UNIFIED APPROACH | INTEGRABLE RELATIVISTIC-EQUATIONS | DISPERSIVE DIELECTRIC FIBERS | CASORATI

Hirota’s bilinear method | Semi-discrete vector NLS equation | Bright-dark soliton | Pfaffian | semi-discrete vector NLS equation | Hirota's bilinear method | INVERSE SCATTERING TRANSFORM | PHYSICS, MATHEMATICAL | OPTICAL PULSES | bright-dark soliton | DISCRETIZATION | TRANSMISSION | WAVES | UNIFIED APPROACH | INTEGRABLE RELATIVISTIC-EQUATIONS | DISPERSIVE DIELECTRIC FIBERS | CASORATI

Journal Article

Laser & Photonics Reviews, ISSN 1863-8880, 03/2016, Volume 10, Issue 2, pp. 177 - 213

One of the challenges of the modern photonics is to develop all‐optical devices enabling increased speed and energy efficiency for transmitting and processing...

amplification | PT‐symmetry | photonics | solitons | nonlinearity | Amplification | Nonlinearity | PT-symmetry | Solitons | Photonics | PHYSICS, CONDENSED MATTER | GAP SOLITONS | PHYSICS, APPLIED | LIGHT | POTENTIALS | DISCRETE SOLITONS | OPTICAL LATTICES | PARITY-TIME SYMMETRY | STATIONARY MODES | REAL SPECTRA | OPTICS | SCATTERING | GAIN | Phase transitions | Broken symmetry | Filtration | Refractivity | Devices | Optical switching | Power efficiency | Energy management | Parity | Active control | Solitary waves | Platinum | Switching | Gain | Symmetry

amplification | PT‐symmetry | photonics | solitons | nonlinearity | Amplification | Nonlinearity | PT-symmetry | Solitons | Photonics | PHYSICS, CONDENSED MATTER | GAP SOLITONS | PHYSICS, APPLIED | LIGHT | POTENTIALS | DISCRETE SOLITONS | OPTICAL LATTICES | PARITY-TIME SYMMETRY | STATIONARY MODES | REAL SPECTRA | OPTICS | SCATTERING | GAIN | Phase transitions | Broken symmetry | Filtration | Refractivity | Devices | Optical switching | Power efficiency | Energy management | Parity | Active control | Solitary waves | Platinum | Switching | Gain | Symmetry

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 10/2004, Volume 73, Issue 248, pp. 1779 - 1799

This paper adresses the construction and study of a Crank-Nicol\-son-type discretization of the two-dimen\-sional linear Schrö...

Linear systems | Error rates | Boundary value problems | Approximation | Wave propagation | Mathematical integrals | Boundary conditions | Fourier transformations | Numerical schemes | Semi-discrete Crank-Nicolson-type scheme | Finite-element methods | Non-reflecting boundary condition | Stability | Schrödinger equation | finite-element methods | MATHEMATICS, APPLIED | non-reflecting boundary condition | Schrodinger equation | stability semi-discrete Crank-Nicolson-type scheme | TRANSPARENT | Numerical Analysis | Mathematics

Linear systems | Error rates | Boundary value problems | Approximation | Wave propagation | Mathematical integrals | Boundary conditions | Fourier transformations | Numerical schemes | Semi-discrete Crank-Nicolson-type scheme | Finite-element methods | Non-reflecting boundary condition | Stability | Schrödinger equation | finite-element methods | MATHEMATICS, APPLIED | non-reflecting boundary condition | Schrodinger equation | stability semi-discrete Crank-Nicolson-type scheme | TRANSPARENT | Numerical Analysis | Mathematics

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 340, Issue 2, pp. 892 - 900

We consider C = A + B where A is selfadjoint with a gap ( a , b ) in its spectrum and B is (relatively) compact. We prove a general result allowing B of...

Jacobi matrices | Schrödinger operators | Eigenvalue bounds | MATHEMATICS, APPLIED | NUMBER | STATES | PERTURBATIONS | FORMULA | SIGMA(H) | MATHEMATICS | H-LAMBDA-W | BRANCHES | eigenvalue bounds | DISCRETE SPECTRUM | Schrodinger operators | SIGN

Jacobi matrices | Schrödinger operators | Eigenvalue bounds | MATHEMATICS, APPLIED | NUMBER | STATES | PERTURBATIONS | FORMULA | SIGMA(H) | MATHEMATICS | H-LAMBDA-W | BRANCHES | eigenvalue bounds | DISCRETE SPECTRUM | Schrodinger operators | SIGN

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 04/2011, Volume 157, Issue 3, pp. 461 - 493

We prove bounds of the form Sigma(is an element of/boolean AND sigma d(H)) dist(e, sigma(e)(H))(1/2) <= L-1 -norm of a perturbation, where I is a gap. Included...

SCHRODINGER OPERATOR | MATHEMATICS | H-LAMBDA-W | PERTURBATIONS | DISCRETE SPECTRUM | EIGENVALUE BRANCHES | 35J10 | 47B36 | 35P15

SCHRODINGER OPERATOR | MATHEMATICS | H-LAMBDA-W | PERTURBATIONS | DISCRETE SPECTRUM | EIGENVALUE BRANCHES | 35J10 | 47B36 | 35P15

Journal Article

15.
Full Text
On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 05/2018, Volume 370, pp. 1 - 13

We consider a one-dimensional discrete nonlinear Schrödinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence...

Perturbation theory | Discrete non-linear Schrödinger | Discrete vortex | Discrete solitons | Current conservation | Lyapunov–Schmidt decomposition | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON LATTICES | PHYSICS, MULTIDISCIPLINARY | STABILITY | EQUATIONS | MULTIBREATHER | PHYSICS, MATHEMATICAL | DYNAMICS | BREATHERS | SPATIAL OPTICAL SOLITONS | Discrete non-linear Schrodinger | Lyapunov-Schmidt decomposition | Physics - Pattern Formation and Solitons

Perturbation theory | Discrete non-linear Schrödinger | Discrete vortex | Discrete solitons | Current conservation | Lyapunov–Schmidt decomposition | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON LATTICES | PHYSICS, MULTIDISCIPLINARY | STABILITY | EQUATIONS | MULTIBREATHER | PHYSICS, MATHEMATICAL | DYNAMICS | BREATHERS | SPATIAL OPTICAL SOLITONS | Discrete non-linear Schrodinger | Lyapunov-Schmidt decomposition | Physics - Pattern Formation and Solitons

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 8/2015, Volume 337, Issue 3, pp. 1241 - 1253

We consider the spectrum of discrete Schrödinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | DISCRETE SCHRODINGER-OPERATORS | CONTINUITY | QUASI-CRYSTALS | POTENTIALS | PHYSICS, MATHEMATICAL

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | DISCRETE SCHRODINGER-OPERATORS | CONTINUITY | QUASI-CRYSTALS | POTENTIALS | PHYSICS, MATHEMATICAL

Journal Article

Physical Review Letters, ISSN 0031-9007, 05/2018, Volume 120, Issue 18, p. 184101

The microcanonical Gross-Pitaevskii (also known as the semiclassical Bose-Hubbard) lattice model dynamics is characterized by a pair of energy and norm...

DISCRETE BREATHERS | PHYSICS, MULTIDISCIPLINARY

DISCRETE BREATHERS | PHYSICS, MULTIDISCIPLINARY

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2015, Volume 268, Issue 5, pp. 1277 - 1307

We consider the three-dimensional Laplacian with a magnetic field created by an infinite rectilinear current bearing a constant current. The spectrum of the...

Discrete spectrum | Magnetic Schrödinger operators | Band functions | 35J10 | 81Q20 | 35P20 | 81Q10 | 47F05 | MATHEMATICS | EDGE CURRENTS | Magnetic Schrodinger operators | POTENTIALS | SPECTRAL PROPERTIES | EIGENVALUE ASYMPTOTICS | SCHRODINGER-OPERATORS | Magnetic fields | Analysis | Mathematics | Spectral Theory | Mathematical Physics | Analysis of PDEs

Discrete spectrum | Magnetic Schrödinger operators | Band functions | 35J10 | 81Q20 | 35P20 | 81Q10 | 47F05 | MATHEMATICS | EDGE CURRENTS | Magnetic Schrodinger operators | POTENTIALS | SPECTRAL PROPERTIES | EIGENVALUE ASYMPTOTICS | SCHRODINGER-OPERATORS | Magnetic fields | Analysis | Mathematics | Spectral Theory | Mathematical Physics | Analysis of PDEs

Journal Article

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, ISSN 1815-2406, 07/2018, Volume 24, Issue 1, pp. 86 - 103

This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods. The analysis...

Error estimates | Time-fractional nonlinear parabolic problems | DIFFERENCE SCHEME | NUMERICAL-METHOD | Linearized schemes | STABILITY | EQUATIONS | DIFFUSION | PHYSICS, MATHEMATICAL | discrete fractional Gronwall type inequality | COLLOCATION | L1-Galerkin FEMs | Mathematics - Numerical Analysis

Error estimates | Time-fractional nonlinear parabolic problems | DIFFERENCE SCHEME | NUMERICAL-METHOD | Linearized schemes | STABILITY | EQUATIONS | DIFFUSION | PHYSICS, MATHEMATICAL | discrete fractional Gronwall type inequality | COLLOCATION | L1-Galerkin FEMs | Mathematics - Numerical Analysis

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 12/2016, Volume 206, Issue 3, pp. 629 - 692

We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and establish relations...

Mathematics, general | Mathematics | MATHEMATICS | ELECTRONIC-ENERGY SPECTRA | QUANTUM DYNAMICS | DYNAMICAL UPPER-BOUNDS | DISCRETE SCHRODINGER-OPERATORS | HOLDER CONTINUITY | DIMENSIONAL QUASI-CRYSTALS | POLYNOMIAL DIFFEOMORPHISMS | POWER-LAW BOUNDS | UNIFORM SPECTRAL PROPERTIES | DENSITY-OF-STATES | Density of states | Properties (attributes) | Entropy | Spectra | Coupling | Quasicrystals | Exponents | Asymptotic properties | Constants | Mathematical models

Mathematics, general | Mathematics | MATHEMATICS | ELECTRONIC-ENERGY SPECTRA | QUANTUM DYNAMICS | DYNAMICAL UPPER-BOUNDS | DISCRETE SCHRODINGER-OPERATORS | HOLDER CONTINUITY | DIMENSIONAL QUASI-CRYSTALS | POLYNOMIAL DIFFEOMORPHISMS | POWER-LAW BOUNDS | UNIFORM SPECTRAL PROPERTIES | DENSITY-OF-STATES | Density of states | Properties (attributes) | Entropy | Spectra | Coupling | Quasicrystals | Exponents | Asymptotic properties | Constants | Mathematical models

Journal Article

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