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- Algebraic eraser (2)
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Articles 1 - 30 of 34
Full-Text Articles in Physical Sciences and Mathematics
Mixed Discriminants, Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein, Sandra Di Rocco, Bernd Strumfels
Mixed Discriminants, Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein, Sandra Di Rocco, Bernd Strumfels
Eduardo Cattani
No abstract provided.
Symmetry-Breaking Bifurcation In The Nonlinear Schrödinger Equation With Symmetric Potentials, E. Kirr, Panos Kevrekidis, D. E. Pelinovsky
Symmetry-Breaking Bifurcation In The Nonlinear Schrödinger Equation With Symmetric Potentials, E. Kirr, Panos Kevrekidis, D. E. Pelinovsky
Panos Kevrekidis
We consider the focusing (attractive) nonlinear Schr\"odinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symmetric, nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non-degenerate local maxima at zero. Under a generic assumption we show that the bifurcation is either subcritical or supercritical pitchfork. In the particular case of double-well potentials with large separation, the power of nonlinearity determines the subcritical or supercritical character of the bifurcation. The results are obtained from a careful analysis of the spectral properties of the …
Multiple Dark-Bright Solitons In Atomic Bose-Einstein Condensates, D. Yan, J. J. Chang, C. Hamner, Panos Kevrekidis, P. Engels, V. Achilleos, D. J. Frantzeskakis, R. Carretero-Gonz´Alez, P. Schmelcher
Multiple Dark-Bright Solitons In Atomic Bose-Einstein Condensates, D. Yan, J. J. Chang, C. Hamner, Panos Kevrekidis, P. Engels, V. Achilleos, D. J. Frantzeskakis, R. Carretero-Gonz´Alez, P. Schmelcher
Panos Kevrekidis
Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton “molecules,” composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. …
Breathers In Oscillator Chains With Hertzian Interactions, Guillaume James, Panos Kevrekidis, Jesus Cuevas
Breathers In Oscillator Chains With Hertzian Interactions, Guillaume James, Panos Kevrekidis, Jesus Cuevas
Panos Kevrekidis
We prove nonexistence of breathers (spatially localized and time-periodic oscillations) for a class of Fermi-Pasta-Ulam lattices representing an uncompressed chain of beads interacting via Hertz's contact forces. We then consider the setting in which an additional on-site potential is present, motivated by the Newton's cradle under the effect of gravity. Using both direct numerical computations and a simplified asymptotic model of the oscillator chain, the so-called discrete p-Schr\"odinger (DpS) equation, we show the existence of discrete breathers and study their spectral properties and mobility. Due to the fully nonlinear character of Hertzian interactions, breathers are found to be much more …
Defeating The Kalka–Teicher–Tsaban Linear Algebra Attack On The Algebraic Eraser, Dorian Goldfeld, Paul E. Gunnells
Defeating The Kalka–Teicher–Tsaban Linear Algebra Attack On The Algebraic Eraser, Dorian Goldfeld, Paul E. Gunnells
Paul Gunnells
The Algebraic Eraser (AE) is a public key protocol for shar- ing information over an insecure channel using commutative and non- commutative groups; a concrete realization is given by Colored Burau Key Agreement Protocol (CBKAP). In this paper, we describe how to choose data in CBKAP to thwart an attack by Kalka–Teicher–Tsaban.
Rabi Flopping Induces Spatial Demixing Dynamics, E. Nicklas, H. Strobel, T. Zibold, C. Gross, B. A. Malomed, Panos Kevrekidis, M. K. Oberthaler
Rabi Flopping Induces Spatial Demixing Dynamics, E. Nicklas, H. Strobel, T. Zibold, C. Gross, B. A. Malomed, Panos Kevrekidis, M. K. Oberthaler
Panos Kevrekidis
We experimentally investigate the mixing and demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena.
Fluctuating And Dissipative Dynamics Of Dark Solitons In Quasicondensates S., S. P. Cockburn, H. E. Nistazakis, T. P. Horikis, Panos Kevrekidis, N. P. Proukakis, D. J. Frantzeskakis
Fluctuating And Dissipative Dynamics Of Dark Solitons In Quasicondensates S., S. P. Cockburn, H. E. Nistazakis, T. P. Horikis, Panos Kevrekidis, N. P. Proukakis, D. J. Frantzeskakis
Panos Kevrekidis
The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark-soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long-lived soliton trajectories within each ensemble of numerical realizations [ S. P. Cockburn et al. Phys. Rev. Lett. 104 174101 (2010)]. Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based …
Resolutions Of The Steinberg Module For Gl(N), Avner Ash, Paul E. Gunnells, Mark Mcconnell
Resolutions Of The Steinberg Module For Gl(N), Avner Ash, Paul E. Gunnells, Mark Mcconnell
Paul Gunnells
We give several resolutions of the Steinberg representation St_n for the general linear group over a principal ideal domain, in particular over Z. We compare them, and use these results to prove that the computations in [AGM4] are definitive. In particular, in [AGM4] we use two complexes to compute certain cohomology groups of congruence subgroups of SL(4,Z). One complex is based on Voronoi's polyhedral decomposition of the symmetric space for SL(n,R), whereas the other is a larger complex that has an action of the Hecke operators. We prove that both complexes allow us to compute the relevant cohomology groups, and …
Dark–Bright Ring Solitons In Bose–Einstein Condensates, J. Stockhofe, Panos Kevrekidis, D. J. Frantzeskakis, P. Schmelcher
Dark–Bright Ring Solitons In Bose–Einstein Condensates, J. Stockhofe, Panos Kevrekidis, D. J. Frantzeskakis, P. Schmelcher
Panos Kevrekidis
We study dark–bright (DB) ring solitons in two-component Bose–Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of a second …
Stationary States Of A Nonlinear Schrödinger Lattice With A Harmonic Trap, V. Achilleos, G. Theocharis, Panos Kevrekidis, N. I. Karachalios, F. K. Diakonos, D. J. Frantzeskakis
Stationary States Of A Nonlinear Schrödinger Lattice With A Harmonic Trap, V. Achilleos, G. Theocharis, Panos Kevrekidis, N. I. Karachalios, F. K. Diakonos, D. J. Frantzeskakis
Panos Kevrekidis
We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that – in the discrete regime – all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is …
Spatial Evolutionary Game Theory: Deterministic Approximations, Decompositions, And Hierarchical Multi-Scale Models, Sung-Ha Hwang
Spatial Evolutionary Game Theory: Deterministic Approximations, Decompositions, And Hierarchical Multi-Scale Models, Sung-Ha Hwang
Open Access Dissertations
Evolutionary game theory has recently emerged as a key paradigm in various behavioral science disciplines. In particular it provides powerful tools and a conceptual framework for the analysis of the time evolution of strategic interdependence among players and its consequences, especially when the players are spatially distributed and linked in a complex social network. We develop various evolutionary game models, analyze these models using appropriate techniques, and study their applications to complex phenomena. In the second chapter, we derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. These generalize the known mean-field ordinary differential equations and provide …
A Mathematical Growth Model Of The Viral Population In Early Hiv-1 Infections, Elena Edi Giorgi
A Mathematical Growth Model Of The Viral Population In Early Hiv-1 Infections, Elena Edi Giorgi
Open Access Dissertations
In this thesis we develop a mathematical model to describe HIV-1 evolution during the first stages of infection (approximately within 40-60 days since onset), when one can assume exponential growth and random accumulation of mutations under a neutral drift. We analyze the Hamming distance (HD) distribution under different models (synchronous and asynchronous) in the absence of selection and recombination. In the second part of the thesis, we introduce recombination and develop a combinatorial approach to estimate the new HD distribution. We conclude describing a T statistic to test significance differences between the HD of two genetic samples, which we derive …
Knot Contact Homology And Open Strings, Jason Frederick Mcgibbon
Knot Contact Homology And Open Strings, Jason Frederick Mcgibbon
Open Access Dissertations
In this thesis, we give a topological interpretation of knot contact homology, by considering intersections of a particular class of chains of open strings with the knot itself. In doing so, we provide evidence toward a differential graded algebra structure on the algebra generated by chains of open strings.
Statistical Methods For Nonlinear Dynamic Models With Measurement Error Using The Ricker Model, David Joseph Resendes
Statistical Methods For Nonlinear Dynamic Models With Measurement Error Using The Ricker Model, David Joseph Resendes
Open Access Dissertations
In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are subject to measurement error, which inevitably leads to biased estimates and adversely affects inference if ignored. In the literature, often convenient distribution assumptions are imposed, readily available estimated measurement error variances are not utilized, or the measurement error is ignored entirely. In this thesis, ways to estimate the parameters of the Ricker model and perform inference while accounting for measurement error are investigated where distribution assumptions are minimized and …
Emergence And Stability Of Vortex Clusters In Bose-Einstein Condensates: A Bifurcation Approach Near The Linear Limit, S. Middelkamp, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, P. Schmelcher
Emergence And Stability Of Vortex Clusters In Bose-Einstein Condensates: A Bifurcation Approach Near The Linear Limit, S. Middelkamp, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, P. Schmelcher
Panos Kevrekidis
We study the existence and stability properties of clusters of alternating charge vortices in Bose-Einstein condensates. It is illustrated that such states emerge from cascades of symmetry-breaking bifurcations that can be analytically tracked near the linear limit of the system via weakly nonlinear few-mode expansions. We present the resulting states that emerge near the first few eigenvalues of the linear limit, and illustrate how the nature of the bifurcations can be used to understand their stability. Rectilinear, polygonal and diagonal vortex clusters are only some of the obtained states while mixed states, consisting of dark solitons and vortex clusters, are …
Discrete Breathers In A Nonlinear Electric Line: Modeling, Computation, And Experiment, F. Palmero, L. Q. English, J. Cuevas, R. Carretero-Gonz´Alez, Panos Kevrekidis
Discrete Breathers In A Nonlinear Electric Line: Modeling, Computation, And Experiment, F. Palmero, L. Q. English, J. Cuevas, R. Carretero-Gonz´Alez, Panos Kevrekidis
Panos Kevrekidis
We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where n-peaked breather solutions …
Dynamics Of Vortex Dipoles In Confined Bose-Einstein Condensates, P. J. Torres, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, P. Schmelcher, D. S. Hall
Dynamics Of Vortex Dipoles In Confined Bose-Einstein Condensates, P. J. Torres, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, P. Schmelcher, D. S. Hall
Panos Kevrekidis
We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.
Guiding-Center Dynamics Of Vortex Dipoles In Bose-Einstein Condensates, S. Middelkamp, P. J. Torres, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´Alez, P. Schmelcher, D. V. Freilich, D. S. Hall
Guiding-Center Dynamics Of Vortex Dipoles In Bose-Einstein Condensates, S. Middelkamp, P. J. Torres, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´Alez, P. Schmelcher, D. V. Freilich, D. S. Hall
Panos Kevrekidis
A quantized vortex dipole is the simplest vortex molecule, comprising two countercirculating vortex lines in a superfluid. Although vortex dipoles are endemic in two-dimensional superfluids, the precise details of their dynamics have remained largely unexplored. We present here several striking observations of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a vortex-particle model that generates vortex line trajectories that are in good agreement with the experimental data. Interestingly, these diverse trajectories exhibit essentially identical quasiperiodic behavior, in which the vortex lines undergo stable epicyclic orbits.
Variational Approximations In Discrete Nonlinear Schrödinger Equations With Next-Nearest-Neighbor Couplings, Panos Kevrekidis, C. Chong, R. Carretero-González, B. A. Malomed
Variational Approximations In Discrete Nonlinear Schrödinger Equations With Next-Nearest-Neighbor Couplings, Panos Kevrekidis, C. Chong, R. Carretero-González, B. A. Malomed
Panos Kevrekidis
Solitons of a discrete nonlinear Schr\"{o}dinger equation which includes the next-nearest-neighbor interactions are studied by means of a variational approximation and numerical computations. A large family of multi-humped solutions, including those with a nontrivial phase structure which are a feature particular to the next-nearest-neighbor interaction model, are accurately predicted by the variational approximation. Bifurcations linking solutions with the trivial and nontrivial phase structures are also captured remarkably well, including a prediction of critical parameter values.
Decompositions Of Two Player Games: Potential, Zero-Sum, And Stable Games, Sung-Ha Hwang, Luc Rey-Bellet
Decompositions Of Two Player Games: Potential, Zero-Sum, And Stable Games, Sung-Ha Hwang, Luc Rey-Bellet
Luc Rey-Bellet
We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal complements which we call anti-potential games and anti-zero-sum games, respectively. Perhaps surprisingly, every anti-potential game comes either from the Rock-Paper-Scissors type games (in the case of symmetric games) or from the Matching Pennies type games (in the case of asymmetric games). Using these decompositions, we prove old (and some new) cycle criteria for potential and zero-sum games (as orthogonality relations between subspaces). …
Nonlinear Excitations, Stability Inversions, And Dissipative Dynamics In Quasi-One-Dimensional Polariton Condensates, J. Cuevas, A. S. Rodrigues, R. Carretero-Gonz´Alez, Panos Kevrekidis, D. J. Frantzeskakis
Nonlinear Excitations, Stability Inversions, And Dissipative Dynamics In Quasi-One-Dimensional Polariton Condensates, J. Cuevas, A. S. Rodrigues, R. Carretero-Gonz´Alez, Panos Kevrekidis, D. J. Frantzeskakis
Panos Kevrekidis
We study the existence, stability, and dynamics of the ground state and nonlinear excitations, in the form of dark solitons, for a quasi-one-dimensional polariton condensate in the presence of nonresonant pumping and nonlinear damping. We find a series of remarkable features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates. For some sizable parameter ranges, the nodeless (“ground”) state becomes unstabletoward the formation of stable nonlinear single- or multi-dark-soliton excitations. It is also observed that for suitable parametric choices, the instability of single dark solitons can nucleate multi-dark-soliton states. Also, for other parametric …
Pt-Symmetric Oligomers: Analytical Solutions, Linear Stability, And Nonlinear Dynamics, K. Li, Panos Kevrekidis
Pt-Symmetric Oligomers: Analytical Solutions, Linear Stability, And Nonlinear Dynamics, K. Li, Panos Kevrekidis
Panos Kevrekidis
In the present work we focus on the case of (few-site) configurations respecting the parity-time (PT) symmetry, i.e., with a spatially odd gain-loss profile. We examine the case of such “oligomers” with not only two sites, as in earlier works, but also the cases of three and four sites. While in the former case of recent experimental interest the picture of existing stationary solutions and their stability is fairly straightforward, the latter cases reveal a considerable additional complexity of solutions, including ones that exist past the linear PT-symmetry breaking point in the case of the trimer, and symmetry-breaking bifurcations, as …
Dark-Bright Gap Solitons In Coupled-Mode One-Dimensional Saturable Waveguide Arrays, Rong Dong, Christian E. Ruter, Detlef Kip, Jesus Cuevas, Panos Kevrekidis, Daohong Song, Jingjun Xu
Dark-Bright Gap Solitons In Coupled-Mode One-Dimensional Saturable Waveguide Arrays, Rong Dong, Christian E. Ruter, Detlef Kip, Jesus Cuevas, Panos Kevrekidis, Daohong Song, Jingjun Xu
Panos Kevrekidis
In the present work, we consider the dynamics of dark solitons as one mode of a defocusing photorefractive lattice coupled with bright solitons as a second mode of the lattice. Our investigation is motivated by an experiment that illustrates that such coupled states can exist with both components in the first gap of the linear band spectrum. This finding is further extended by the examination of different possibilities from a theoretical perspective, such as symbiotic ones where the bright component is supported by states of the dark component in the first or second gap, or nonsymbiotic ones where the bright …
Nonlinear Waves In Lattices: Past, Present, Future, Panos Kevrekidis
Nonlinear Waves In Lattices: Past, Present, Future, Panos Kevrekidis
Panos Kevrekidis
In the present work, we attempt a brief summary of various areas where non-linear waves have been emerging in the phenomenology of lattice dynamical systems. These areas include non-linear optics, atomic physics, mechanical systems, electrical lattices, non-linear metamaterials, plasma dynamics and granular crystals. We give some of the recent developments in each one of these areas and speculate on some of the potentially interesting directions for future study.
Symmetry Breaking, Coupling Management, And Localized Modes In Dual-Core Discrete Nonlinear-Schrödinger Lattices, H. Susanto, Panos Kevrekidis, F. Kh. Abdullaev, Boris A. Malomed
Symmetry Breaking, Coupling Management, And Localized Modes In Dual-Core Discrete Nonlinear-Schrödinger Lattices, H. Susanto, Panos Kevrekidis, F. Kh. Abdullaev, Boris A. Malomed
Panos Kevrekidis
We introduce a system of two linearly coupled discrete nonlinear Schr\"{o}dinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC). Using an averaging procedure based on the multiscale method, we derive a system of averaged (autonomous) equations, which take the form of coupled DNLSEs with additional nonlinear coupling terms of the four-wave-mixing type. We identify stability regions for fundamental onsite discrete symmetric solitons (single-site modes with equal norms in both components), as well as for two-site in-phase and twisted modes, the in-phase ones being completely unstable. The …
Quasidiscrete Microwave Solitons In A Split-Ring-Resonator-Based Left-Handed Coplanar Waveguide, G. P. Veldes, J. Cuevas, Panos Kevrekidis, D. J. Frantzeskakis
Quasidiscrete Microwave Solitons In A Split-Ring-Resonator-Based Left-Handed Coplanar Waveguide, G. P. Veldes, J. Cuevas, Panos Kevrekidis, D. J. Frantzeskakis
Panos Kevrekidis
We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split-ring resonators. By considering the relevant transmission line analog, we derive a nonlinear lattice model which is studied analytically by means of a quasidiscrete approximation. We derive a nonlinear Schrödinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasidiscrete microwave solitons. Our numerical findings are in good agreement with the analytical …
Tunable Vibrational Band Gaps In One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells, N. Boechler, J. Yang, G. Theocharis, Panos Kevrekidis, C. Daraio
Tunable Vibrational Band Gaps In One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells, N. Boechler, J. Yang, G. Theocharis, Panos Kevrekidis, C. Daraio
Panos Kevrekidis
We investigate the tunable vibration filtering properties of statically compressed one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (sphere-cylinder-sphere) in which the length of the cylinder is varied systematically. We investigate the response of these granular crystals, given small amplitude dynamic displacements relative to those due to the static compression, and characterize their linear frequency spectrum. We find good agreement between theoretical dispersion relation analysis (for infinite systems), state-space analysis (for finite systems), and experiments. We report the observation of three distinct …
Dark-Bright Discrete Solitons: A Numerical Study Of Existence, Stability And Dynamics, A. Alvarez, J. Cuevas, F. R. Romero, Panos Kevrekidis
Dark-Bright Discrete Solitons: A Numerical Study Of Existence, Stability And Dynamics, A. Alvarez, J. Cuevas, F. R. Romero, Panos Kevrekidis
Panos Kevrekidis
In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions …
Radial Standing And Self-Similar Waves For The Hyperbolic Cubic Nls In 2d, Panos Kevrekidis, Andrea R. Nahmod, Chongchun Zeng
Radial Standing And Self-Similar Waves For The Hyperbolic Cubic Nls In 2d, Panos Kevrekidis, Andrea R. Nahmod, Chongchun Zeng
Panos Kevrekidis
In this note we propose a new set of coordinates to study the hyperbolic or non-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically radial standing waves, as well as hyperbolically radial self-similar solutions. Many of the arguments can easily be adapted to more general nonlinearities.
Control Of The Symmetry Breaking In Double-Well Potentials By The Resonant Nonlinearity Management, H. E. Nistazakis, B. A. Malomed, Panos Kevrekidis, D. J. Frantzeskakis
Control Of The Symmetry Breaking In Double-Well Potentials By The Resonant Nonlinearity Management, H. E. Nistazakis, B. A. Malomed, Panos Kevrekidis, D. J. Frantzeskakis
Panos Kevrekidis
We introduce a one-dimensional model of Bose–Einstein condensates (BECs), combining the double-well potential, which is a usual setting for the onset of spontaneous-symmetry-breaking (SSB) effects, and time-periodic modulation of the nonlinearity, which may be implemented by means of the Feshbach-resonance-management (FRM) technique. Both cases of the nonlinearity that is repulsive or attractive on the average are considered. In the former case, the main effect produced by the application of the FRM is spontaneous self-trapping of the condensate in either of the two potential wells in parameter regimes where it would remain untrapped in the absence of the management. In the …