Related papers: Analysis of interaction dynamics and rogue wave lo…
In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in…
Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…
We investigate how localized inhomogeneity affects the geometry and stability of migratory bird formations. We use a lifting-line model with a horseshoe-vortex representation to describe the longitudinal dynamics of aerodynamic…
Theoretical and numerical studies are presented of the nonlinear amplitude modulation of dust-acoustic (DA) waves propagating in an unmagnetized three component, weakly-coupled, fully ionized plasma consisting of electrons, positive ions…
Being considered as a prototype for description of oceanic rogue waves (RWs), the Peregrine breather solution of the nonlinear Schr\"odinger equation (NLS) has been recently observed and intensely investigated experimentally in particular…
In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in…
We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
We study transmission stability and dynamics of pulse amplitudes in $N$-channel soliton-based optical waveguide systems, taking into account second-order dispersion, Kerr nonlinearity, delayed Raman response, and frequency dependent linear…
This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot…
We study localization and control for unstable systems under coarse, single-bit sensing. Motivated by understanding the fundamental limitations imposed by such minimal feedback, we identify sufficient conditions under which the initial…
We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next,…
The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of…
Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…
Over the past decade, the rogue wave debate has stimulated the comparison of predictions and observations among different branches of wave physics, particularly between hydrodynamics and optics, in situations where analogous dynamical…
We present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear…
A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
Ocean dynamics constitute a source of incertitude in determining the ocean's role in complex climatic phenomena. Current observation systems have limitations in achieving sufficiently statistical precision for three-dimensional oceanic…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped…