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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
Journal Article
by Papp, E
2007, ISBN 9812706380, xiii, 262
Book
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
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
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
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 09/2017, Volume 13
Journal Article
Laser & Photonics Reviews, ISSN 1863-8880, 03/2016, Volume 10, Issue 2, pp. 177 - 213
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
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
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 05/2018, Volume 370, pp. 1 - 13
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
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
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
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
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 12/2016, Volume 206, Issue 3, pp. 629 - 692
Journal Article
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