arXiv subjects

J. Cuevas-Maraver

Publications and source records attributed to J. Cuevas-Maraver.

At least 19 recordsLinked to original sources

arXiv2026

Solitary waves and vortices in a Nonlinear Schrödinger equation with ponderomotive nonlinearity

In the present work we revisit a ponderomotive nonlinearity model used to examine self-trapped laser beams in plasma. Upon briefly considering the exact stationary 1D solutions of the model, we extend considerations to two spatial dimensions where we find both solitonic and vortical structures. The solitary waves localized in both directions are found to be spectrally stable. However, all other structures that we consider in this model, including line solitons -- which are homogeneous 2D extensions of 1D solitons -- and vortices of topological charge S=1 and S=2 are found to be spectrally unstable. The focal point of our studies then turns to the examination of the collisions of the stable two-dimensional solitary waves for which we map a two-parameter space of soliton speeds and frequencies, in terms of the potential outcomes. While the standard scenarios of merger, inelastic collision leading to separation, separation that leaves behind a localized pulse are all possible, the intriguing outcome that we highlight here is that of a longitudinal collision yielding a transverse spliting of the solitons, either with or without a localized pulse remnant.

nlin.PS↗

arXiv2025

On a Klein-Gordon Reduction for Oscillons

In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to first and third harmonics, which leads to a reduced partial differential equation (PDE) system whose steady states are candidates for the original PDE oscillons. We analyze the steady states of this model and their stability, including via tools such as index theory. We develop suitable functionals needed for the study of such stationary states, as well as an analogue of the famous Vakhitov-Kolokolov criterion for a quantity whose change of monotonicity reflects a change of stability. Then, we test the relevant predictions, over the full range of oscillon frequencies, through systematic numerical computations of both the reduced model, its steady states and stability, and also of the original PDE model, identifying its time-periodic oscillon solution. Our results yield some significant connections with previous studies, but also some fundamental new insights both on the reduced system and the dynamics of the original system.

nlin.PS↗

arXiv2025

On the Fractional Dynamics of Kinks in sine-Gordon Models

In the present work we explore the dynamics of single kinks, kink-anti-kink pairs and bound states in the prototypical fractional Klein-Gordon example of the sine-Gordon equation. In particular, we modify the order $β$ of the temporal derivative to that of a Caputo fractional type and find that, for $1<β<2$, this imposes a dissipative dynamical behavior on the coherent structures. We also examine the variation of a fractional Riesz order $α$ on the spatial derivative. Here, depending on whether this order is below or above the harmonic value $α=2$, we find, respectively, monotonically attracting kinks, or non-monotonic and potentially attracting or repelling kinks, with a saddle equilibrium separating the two. Finally, we also explore the interplay of the two derivatives, when both Caputo temporal and Riesz spatial derivatives are involved.

nlin.PS↗

arXiv2024

Practical identifiability and parameter estimation of compartmental epidemiological models

Practical parameter identifiability in ODE-based epidemiological models is a known issue, yet one that merits further study. It is essentially ubiquitous due to noise and errors in real data. In this study, to avoid uncertainty stemming from data of unknown quality, simulated data with added noise are used to investigate practical identifiability in two distinct epidemiological models. Particular emphasis is placed on the role of initial conditions, which are assumed unknown, except those that are directly measured. Instead of just focusing on one method of estimation, we use and compare results from various broadly used methods, including maximum likelihood and Markov Chain Monte Carlo (MCMC) estimation. Among other findings, our analysis revealed that the MCMC estimator is overall more robust than the point estimators considered. Its estimates and predictions are improved when the initial conditions of certain compartments are fixed so that the model becomes globally identifiable. For the point estimators, whether fixing or fitting the that are not directly measured improves parameter estimates is model-dependent. Specifically, in the standard SEIR model, fixing the initial condition for the susceptible population S(0) improved parameter estimates, while this was not true when fixing the initial condition of the asymptomatic population in a more involved model. Our study corroborates the change in quality of parameter estimates upon usage of pre-peak or post-peak time-series under consideration. Finally, our examples suggest that in the presence of significantly noisy data, the value of structural identifiability is moot.

stat.ME↗

arXiv2023

Breathers in the fractional Frenkel-Kontorova model

In the present chapter, we explore the possibility of a Frenkel-Kontorova (discrete sine-Gordon) model to bear interactions that decay algebraically with space, inspired by the continuum limit of the corresponding fractional derivative. In such a setting, we revisit the realm of discrete breathers including onsite, intersite and out-of-phase ones and identify their power-law spatial decay, as well as explore their corresponding stability analysis, by means of Floquet multipliers. The relevant stability is also explored parametrically as a function of the frequency and connected to stability criteria for breather dependence of energy vs. frequency. Finally, by suitably perturbing the breathers, we also generate moving waveforms and explore their radiation and potential robustness.

nlin.PS↗

arXiv2023

Existence, stability and spatio-temporal dynamics of time-quasiperiodic solutions on a finite background in discrete nonlinear Schrödinger models

In the present work we explore the potential of models of the discrete nonlinear Schrödinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously shown to exist in the vicinity of the anti-continuum, vanishing coupling limit of the model. We then use numerical continuation to illustrate their persistence for finite coupling, as well as to explore their spectral stability. We obtain an intricate bifurcation diagram showing a progression of such solutions from simpler ones bearing single- and two-site excitations to more complex, multi-site ones with a direct connection of the branches of the self-focusing and self-defocusing nonlinear regime. We further probe the variation of the solutions obtained towards the limit of vanishing frequency for both signs of the nonlinearity. Our analysis is complemented by exploring the dynamics of the solutions via direct numerical simulations.

nlin.PS↗

arXiv2023

Discrete Breathers in Klein-Gordon Lattices: a Deflation-Based Approach

Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend deflation to discover new periodic orbits in nonlinear dynamical lattices. We employ our extension to identify discrete breathers, which are generic exponentially localized, time-periodic solutions of such lattices. We compare different approaches to using deflation for periodic orbits, including ones based on a Fourier decomposition of the solution, as well as ones based on the solution's energy density profile. We demonstrate the ability of the method to obtain a wide variety of multibreather solutions without prior knowledge about their spatial profile.

nlin.PS↗

arXiv2023

Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants

We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves.

q-bio.PE↗

arXiv2023

Solitary wave billiards

In the present work we explore the concept of solitary wave billiards. I.e., instead of a point particle, we examine a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. Furthermore, the nature of the scattering of the deformable solitary wave particle is elucidated on the basis of a negative Goos-Hänchen effect which, in addition to a trajectory shift, also results in an effective shrinkage of the billiard domain.

nlin.PS↗

arXiv2022

Scattering-induced splitting of solitons in the discrete NLS equation with saturable nonlinearity

We study systematically the scattering of solitons on localized impurities in the discrete nonlinear Schrödinger (DNLS) equation with a saturable nonlinearity. We show that, apart from the generic scenario of the outcome of the scattering process, namely the emergence of a reflected and a transmitted soliton, other effects can occur. In particular, it is found that, in the case of an attractive impurity, a soliton trapped at the impurity can coexist with the reflected and transmitted ones. This effect, which resembles the behaviour of a quantum particle interacting with a narrow impurity, has not previously reported for discrete setting. Parameter regimes are explored for determining soliton splitting on the impurity with special attention to equal soliton splitting.

nlin.PS↗

arXiv2022

Discrete breathers in a mechanical metamaterial

We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we identify parameter regimes in which this system may possess discrete breather solutions with frequencies inside the gap between optical and acoustic dispersion bands. We compute numerically exact solutions of this type for several different parameter regimes and investigate their properties and stability. Our findings demonstrate that upon appropriate parameter tuning within experimentally tractable ranges, the system exhibits a plethora of discrete breathers, with multiple branches of solutions that feature period-doubling and symmetry-breaking bifurcations, in addition to other mechanisms of stability change such as saddle-center and Hamiltonian Hopf bifurcations. The relevant stability analysis is corroborated by direct numerical computations examining the dynamical properties of the system and paving the way for potential further experimental exploration of this rich nonlinear dynamical lattice setting.

nlin.PS↗

arXiv2022

The role of mobility in the dynamics of the COVID-19 epidemic in Andalusia

Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time dependent data, but also discussing the comparison for our case example with a gravity model, as well as with the dynamics in the absence of mobility. Our main finding is that mobility is key towards a quantitative understanding of the emergence of the second wave of the pandemic and that the most accurate way to capture it involves dynamic (rather than static) inclusion of time-dependent mobility matrices based on cell-phone data. Alternatives bearing no mobility are unable to capture the trends revealed by the data in the context of the metapopulation model considered herein.

physics.soc-ph↗

arXiv2022

Mixed dispersion nonlinear Schrödinger equation in higher dimensions: theoretical analysis and numerical computations

In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schr{ö}dinger class with a combination of a focusing biharmonic operator with either an isotropic or an anisotropic defocusing Laplacian operator (at the linear level) and power-law nonlinearity. Examining principally the prototypical example of dimension $d=2$, we find that instability arises beyond a certain threshold coefficient of the Laplacian between the cubic and quintic cases, while all solutions are stable for powers below the cubic. Above the quintic, and up to a critical nonlinearity exponent $p$, there exists a progressively narrowing range of stable frequencies. Finally, above the critical $p$ all solutions are unstable. The picture is rather similar in the anisotropic case, with the difference that even before the cubic case, the numerical computations suggest an interval of unstable frequencies. Our analysis generalizes the relevant observations for arbitrary combinations of Laplacian prefactor $b$ and nonlinearity power $p$.

nlin.PS↗

arXiv2022

Backcasting COVID-19: A Physics-Informed Estimate for Early Case Incidence

It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian Process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea, and Brazil. We assume that the second wave was more accurately monitored and hence that it can be trusted. We then construct a manifold diffeomorphic to that of the implied original dynamical system, using fatalities or hospitalizations only. Finally, we restrict the diffeomorphism to the reported cases coordinate of the dynamical system. Our main finding is that in the European countries studied, the actual cases are under-reported by as much as 50\%. On the other hand, in South Korea -- which had an exemplary and proactive mitigation approach -- a far smaller discrepancy between the actual and reported cases is predicted, with an approximately 17\% predicted under-estimation. We believe that our backcasting framework is applicable to other epidemic outbreaks where (due to limited or poor quality data) there is uncertainty around the actual cases.

q-bio.QM↗

arXiv2021

Moving discrete breathers in a $β$-FPU lattice revisited

In the present work we revisit the existence, stability and dynamical properties of moving discrete breathers in $β$-FPU lattices. On the existence side, we propose a numerical procedure, based on a continuation along a sequence of velocities, that allows to systematically construct breathers traveling more than one lattice site per period. On the stability side, we explore the stability spectrum of the obtained waveforms via Floquet analysis and connect it to the energy-frequency bifurcation diagrams. We illustrate in this context examples of the energy being a multivalued function of the frequency, showcasing the coexistence of different moving breathers at the same frequency. Finally, we probe the moving breather dynamics and observe how the associated instabilities change their speed, typically slowing them down over longtime simulations.

nlin.PS↗

arXiv2021

Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples

We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain and the mainland of Greece. We start with a 0D compartmental epidemiological model consisting of Susceptible, Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and deceased populations. We emphasize the importance of the viral latent period and the key role of an asymptomatic population. We optimize model parameters for both regions by comparing predictions to the cumulative number of infected and total number of deaths via minimizing the $\ell^2$ norm of the difference between predictions and observed data. We consider the sensitivity of model predictions on reasonable variations of model parameters and initial conditions, addressing issues of parameter identifiability. We model both pre-quarantine and post-quarantine evolution of the epidemic by a time-dependent change of the viral transmission rates that arises in response to containment measures. Subsequently, a spatially distributed version of the 0D model in the form of reaction-diffusion equations is developed. We consider that, after an initial localized seeding of the infection, its spread is governed by the diffusion (and 0D model "reactions") of the asymptomatic and symptomatically infected populations, which decrease with the imposed restrictive measures. We inserted the maps of the two regions, and we imported population-density data into COMSOL, which was subsequently used to solve numerically the model PDEs. Upon discussing how to adapt the 0D model to this spatial setting, we show that these models bear significant potential towards capturing both the well-mixed, 0D description and the spatial expansion of the pandemic in the two regions. Veins of potential refinement of the model assumptions towards future work are also explored.

q-bio.PE↗

arXiv2020

Breather stripes and radial breathers of the two-dimensional sine-Gordon equation

We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically computed Floquet spectrum of the stripe is compared to analytical predictions developed by means of multiple-scale perturbation theory showing good agreement in the long-wavelength limit. By means of direct simulations, it is found that the instability leads to a breakup of the quasi-1D breather in a chain of interacting 2D radial breathers that appear to be fairly robust in the dynamics. The stability and dynamics of radial breathers in a finite domain are studied in detail by means of numerical methods. Different families of such solutions are identified. They develop small-amplitude spatially oscillating tails ("nanoptera") through a resonance of higher-order breather's harmonics with linear modes ("phonons") belonging to the continuous spectrum. These results demonstrate the ability of the 2D sG model within our finite domain computations to localize energy in long-lived, self-trapped breathing excitations.

nlin.PS↗

arXiv2020

A quantitative framework for exploring exit strategies from the COVID-19 lockdown

Following the highly restrictive measures adopted by many countries for combating the current pandemic, the number of individuals infected by SARS-CoV-2 and the associated number of deaths is steadily decreasing. This fact, together with the impossibility of maintaining the lockdown indefinitely, raises the crucial question of whether it is possible to design an exit strategy based on quantitative analysis. Guided by rigorous mathematical results, we show that this is indeed possible: we present a robust numerical algorithm which can compute the cumulative number of deaths that will occur as a result of increasing the number of contacts by a given multiple, using as input only the most reliable of all data available during the lockdown, namely the cumulative number of deaths.

q-bio.PE↗