Related papers: Multifaceted nonlinear dynamics in $\mathcal{PT}$-…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic non-Newtonian fluid mechanics simulators in performing systematic stability/bifurcation analysis. The timestepper approach to bifurcation analysis of…
Driven-dissipative light-matter systems can exhibit collective nonequilibrium phenomena due to loss and gain processes on the one hand and effective photon-photon interactions on the other hand. As generic example we study a bosonic lattice…
We prove nonlinear stability of the Larson-Penston family of self-similarly collapsing solutions to the isothermal Euler-Poisson system. Our result applies to radially symmetric perturbations and it is the first full nonlinear stability…
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…
Based on a system-reservoir model and an appropriate choice of nonlinear coupling, we have explored the microscopic quantum generalization of classical Li\'{e}nard systems. Making use of oscillator coherent states and canonical thermal…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
We present the time dynamics of twisted quantum states. We find an explicit connection between the well-known stationary Landau state and an evolving twisted state, even when the Hamiltonian accounts for linear energy dissipation. Utilizing…
In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…
Employing a two-species Cahn-Hilliard model with nonreciprocal interactions we show that the interplay of nonreciprocity and conservation laws results in the robust coexistence of uniform stationary and oscillatory phases as well as of…
We describe linear and nonlinear modes in a ring-shaped waveguide with localized gain and dissipation modeled by two Dirac $\delta$ functions located symmetrically. The strengths of the gain and dissipation are equal, i.e., the system obeys…
In the Hermitian regime, the Wannier-Stark ladder characterizes the eigenstates of an electron in a periodic potential with an applied static electric field. In this work, we extend this concept to the complex regime for a periodic…
We give an example of a simple mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. This system is a linearized plane pendulum with…
Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work,…
Recently [Phys. Rev. Lett. {\bf 106}, 093902 (2011)] it has been shown that $\mathcal{PT}$-symmetric scattering systems with balanced gain and loss, undergo a transition from $\mathcal{PT}$-symmetric scattering eigenstates, which are norm…
Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model…
We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…
We consider the time-dependent nonlinear system $\dot q(t)=u(t)X(q(t))+(1-u(t))Y(q(t))$, where $q\in\R^2$, $X$ and $Y$ are two %$C^\infty$ smooth vector fields, globally asymptotically stable at the origin and $u:[0,\infty)\to\{0,1\}$ is an…
The phenomenon of intrinsic localization in discrete nonlinear extended systems, i.e. the (generic) existence of discrete breathers, is shown to be not restricted to periodic solutions but it also extends to more complex (chaotic) dynamical…