Related papers: Exit manifolds for lattice differential equations
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic cells on a substrate. We establish uniqueness of solutions to the sharp…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…
We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, near the continuous limit.We construct a family of solutions…
Propagation of transition fronts in models of coupled oscillators with non-degenerate on-site potential is usually considered in terms of travelling waves. We show that the system dynamics can be reformulated as an implicit map structure,…
We study stability of travelling wave solutions to Korteweg--de Vries type equations which has the fractional dispersion and integer-indices double power nonlinearities. It may depend on parity combinations of the two indices and the…
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 numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes…
We consider a flat lattice of dipoles modeled by harmonic oscillators interacting with the electromagnetic field in dipole approximation. Eliminating the variables from the coupled equations of motion, we come to effective Maxwell…
We study traveling wave solutions for a nonlinear Schr\"odinger system with quadratic interaction. For the non mass resonance case, the system has no Galilean symmetry, which is of particular interest in this paper. We construct traveling…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
In this note, we investigate a doubly nonlinear diffusion equation in the slow diffusion regime. We prove stability of the pressure of solutions that are close to traveling wave solutions in a homogeneous Lipschitz sense. We derive…
Nonreciprocal interactions, in which action-reaction symmetry is broken, provide a powerful route to collective dynamics that cannot be captured by equilibrium free-energy minimisation. Here, we introduce and analyse a two-species…
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 Cauchy problem for two dimensional difference wave operators is considered with potentials and initial data supported in a bounded region. The large time asymptotic behavior of solutions is obtained. In contrast to the continuous case…
Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to…
We investigate the existence and stability of travelling wave solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric…
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…