Related papers: Periodically generated propagating pulses
We present the derivation of generic equations describing the long gravity waves in incompressible fluid with decaying effect. We show that in this theory the only restriction to the surface deviation is connected with the stability…
The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and…
In this paper we consider a class of nonlinear wave equation with $x$-dependent coefficients and prove existence of families of time-periodic solutions under the general boundary conditions. Such a model arises from the forced vibrations of…
The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We further generalize the generalized short pulse equation studied recently in [Commun. Nonlinear Sci. Numer. Simulat. 39 (2016) 21-28; arXiv:1510.08822], and find in this way two new integrable nonlinear wave equations which are…
An electromagnetic truncated Gaussian pulse propagates through a waveguide with piecewise different dielectric constants. The waveguide contains a barrier, namely a region of a lower dielectric constant compared to the neighboring regions.…
A non-Gaussian Hardy equation is studied with a non-linearity of Osgood-type growth. A fractional derivative in time is incorporated for the first time in an research of this type. Existence of local and global solutions are established by…
Modeling the propagation of gravitational waves (GWs) through matter is complicated by the gauge freedom of linearized gravity in that once nonlinearities are taken into consideration, gauge artifacts can cause spurious acceleration of the…
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given…
In this manuscript we prove global existence and linear asymptotic behavior of small solutions to nonlinear wave equations. We assume that the quadratic part of the nonlinearity satisfies a non-resonant condition which is a generalization…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
We study the thermalization of the classical Klein-Gordon equation under a u^4 interaction. We numerically show that even in the presence of strong nonlinearities, the local thermodynamic equilibrium state exhibits a weakly nonlinear…
A novel model of wave turbulence is presented which allows to explain in the same frame various nonlinear wave phenomena: intermittency, form and direction of the energy cascades, formation of a zero-frequency band with non-zero energy,…
Asymptotically nonlocal field theories interpolate between Lee-Wick theories with multiple propagator poles, and ghost-free nonlocal theories. Previous work on asymptotically nonlocal scalar, Abelian, and non-Abelian gauge theories has…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form…
We study the k-space fluctuations of the waveaction about its mean spectrum in the turbulence of dispersive waves. We use a minimal model based on the Random Phase Approximation (RPA) and derive evolution equations for the arbitrary-order…
We show that useful non-instantaneous nonlinear phase shifts can be obtained from cascaded quadratic processes in the presence of group velocity mismatch. The two-field nature of the process permits responses that can be effectively…