Related papers: Periodic travelling waves in convex Klein-Gordon c…
We consider a scalar Hamiltonian nonlinear wave equation formulated on networks; this is a non standard problem because these domains are not locally homeomorphic to any subset of the Euclidean space. More precisely, we assume each edge to…
Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the…
This paper focuses on the analysis of stratified steady periodic water waves that contain stagnation points. The initial step involves transforming the free-boundary problem into a quasilinear pseudodifferential equation through a conformal…
In this paper, we examine some basic properties of the multiple-Sine-Gordon (MSG) systems, which constitute a generalization of the celebrated sine-Gordon (SG) system. We start by showing how MSG systems can be viewed as a general class of…
For a two parameter family of two-dimensional piecewise linear maps and for every natural number $ n $ we prove not only the existence of intervals of parameters for which the respective maps are $ n $ times renormalizable but also we show…
Ratchet models are prominent candidates to describe the transport phenomenum in nature in the absence of external bias. This work analyzes the parameter space of a discrete ratchet model and gives direct connections between chaotic domains…
The Conley theory has a tool to guarantee the existence of periodic trajectories in isolating neighborhoods of semi-dynamical systems. We prove that the positive trajectories generated by a piecewise-smooth vector field $Z=(X, Y)$ defined…
We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all…
We consider static solutions of the sine-Gordon theory defined on a cylinder, which can be either periodic or quasi-periodic in space. They are described by the different modes of a simple pendulum moving in an inverted effective potential…
We present the recent result [8] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the first existence result of quasi-periodic water waves solutions…
We study Hamiltonian difference schemes for scalar conservation laws with monotone flux function and establish the existence of a three-parameter family of periodic travelling waves (wavetrains). The proof is based on an integral equation…
In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive.…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding…
The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An…
We investigate kinetic energy properties of an irrotational deep-water Stokes wave. By introducing a conformal hodograph transform, we perform complex analysis in the new variables, and show that the existence of the streamline time-period…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…
We consider the quadratic and cubic KP - I and NLS models in $1+2$ dimensions with periodic boundary conditions. We show that the spatially periodic travelling waves (with period $K$) in the form $u(t,x,y)=\vp(x-c t)$ are spectrally and…
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…
We study the periodic Schr\"odinger-Korteweg de Vries system. We describe the two-parametetric family of $2T$ periodic traveling waves of dnoidal type. The main objective of the paper is to establish their spectral stability with respect to…