Física Aplicada I

URI permanente para esta comunidadhttps://hdl.handle.net/11441/10848

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Floquet solitons in square lattices: Existence, stability, and dynamics
(American Physical Society, 2022-04) Parker, Ross; Aceves, Alejandro; Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Universidad de Sevilla. Departamento de Física Aplicada I; Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía and FEDER (EU) P18-RT-3480; Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía and FEDER (EU) US-1380977; MICINN and AEI PID2019-110430GB-C21; MICINN and AEI PID2020-112620GB-I00; Universidad de Sevilla. FQM280: Física no Lineal
In the present work, we revisit a recently proposed and experimentally realized topological two-dimensional lattice with periodically time-dependent interactions. We identify the fundamental solitons, previously observed in experiments and direct numerical simulations, as exact, exponentially localized, periodic in time solutions. This is done for a variety of phase-shift angles of the central nodes upon an oscillation period of the coupling strength. Subsequently, we perform a systematic Floquet stability analysis of the relevant structures. We analyze both their point and their continuous spectrum and find that the solutions are generically stable, aside from the possible emergence of complex quartets due to the collision of bands of continuous spectrum. The relevant instabilities become weaker as the lattice size gets larger. Finally, we also consider multisoliton analogs of these Floquet states, inspired by the corresponding discrete nonlinear Schrödinger (DNLS) lattice. When exciting initially multiple sites in phase, we find that the solutions reflect the instability of their DNLS multi-soliton counterparts, while for configurations with multiple excited sites in alternating phases, the Floquet states are spectrally stable, again analogously to their DNLS counterparts.
Revisiting multi-breathers in the discrete Klein–Gordon equation: a spatial dynamics approach
(IOP Publishing, 2022-11) Parker, Ross; Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Aceves, Alejandro; Universidad de Sevilla. Departamento de Física Aplicada I; Universidad de Sevilla. FQM280: Física no Lineal
We consider the existence and spectral stability of multi-breather structures in the discrete Klein–Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a finite-dimensional Hilbert space consisting of the first M Fourier modes, for arbitrary M. On this approximate system, we then take a spatial dynamics approach and use Lin’s method to construct multi-breathers from a sequence of well-separated copies of the primary, single-site breather. We then locate the eigenmodes in the Floquet spectrum associated with the interaction between the individual breathers of such multi-breather states by reducing the spectral problem to a matrix equation. Expressions for these eigenmodes for the approximate, finite-dimensional system are obtained in terms of the primary breather and its kernel eigenfunctions, and these are found to be in very good agreement with the numerical Floquet spectrum results. This is supplemented with results from numerical timestepping experiments, which are interpreted using the spectral computations.
Standing and traveling waves in a model of periodically modulated one-dimensional waveguide arrays
(American Physical Society, 2023-08) Parker, Ross; Aceves, Alejandro; Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Universidad de Sevilla. Departamento de Física Aplicada I; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Junta de Andalucía; Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla. FQM280: Física no Lineal
In the present work we study coherent structures in a one-dimensional discrete nonlinear Schrödinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions show that, depending on the power, the system exhibits two fundamentally different behaviors. At low power, initial conditions with intensity concentrated in a single site give rise to transport, with the energy moving unidirectionally along the lattice, whereas high-power initial conditions yield stationary solutions. We explain these two behaviors, as well as the nature of the transition between the two regimes, by analyzing a simpler model where the couplings between waveguides are given by step functions. For the original model, we numerically construct both stationary and moving coherent structures, which are solutions reproducing themselves exactly after an integer multiple of the coupling period. For the stationary solutions, which are true periodic orbits, we use Floquet analysis to determine the parameter regime for which they are spectrally stable. Typically, the traveling solutions are characterized by having small-amplitude oscillatory tails, although we identify a set of parameters for which these tails disappear. These parameters turn out to be independent of the lattice size, and our simulations suggest that for these parameters, numerically exact traveling solutions are stable.

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Examinando Física Aplicada I por Autor "Aceves, Alejandro"