Related papers: Longtime behavior of coupled wave equations for se…
The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order…
We introduce a model description of femtosecond laser induced desorption at surfaces. The substrate part of the system is taken into account as a (possibly semi-infinite) linear chain. Here, being especially interested in the early stages…
Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of…
A new approach to design wavelength insensitive optical power splitter is presented. First coupled-mode theory is cast in operatorial form. This allows to solve the equivalent of coupled differential equations as simple limits. The…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
This paper is devoted to the initial value problems for semilinear wave equations of derivative type with spatial weights in one space dimension. The lifespan estimates of classical solutions are quite different from those for nonlinearity…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…
The open question, which seems to be also the final part, in terms of studying the Cauchy problem for the weakly coupled system of damped wave equations or reaction-diffusion equations, is so far known as the sharp lifespan estimates in the…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
Arrays of coupled semiconductor lasers are systems possessing radically complex dynamics that makes them useful for numerous applications in beam forming and beam shaping. In this work, we investigate the spatial controllability of…
We study layered systems and heterostructures of s-wave superconductors by means of a suitable generalization of Dynamical Mean-Field Theory. In order to reduce the computational effort, we consider an embedding scheme in which a relatively…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
Semiclassical equations of lasing dynamics are re-derived for a lasing medium in a cavity with a spatially non-uniform dielectric constant. It is shown that the non-uniformity causes a radiative coupling between modes of the empty cavity.…
We study semilinear wave equations with Ginzburg-Landau type nonlinearities multiplied by a factor $\epsilon^{-2}$, where $\epsilon>0$ is a small parameter. We prove that for suitable initial data, solutions exhibit energy concentration…
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
In this paper, we overview the recent progresses on the lifespan estimates of classical solutions of the initial value problems for nonlinear wave equations in one space dimension. There are mainly two directions of the developments on the…