Traveling waves and Compactons in Phase Oscillator Lattices

TL;DR

This paper investigates various traveling wave solutions in a chain of dispersively coupled phase oscillators, including compactons, kovatons, and semi-compact waves, analyzing their stability through numerical simulations.

Contribution

It introduces a comprehensive analysis of different wave types in phase oscillator lattices using both analytical and numerical methods, including a new semi-compact wave class.

Findings

Identification of compactons, kovatons, and semi-compact waves in the lattice.

Demonstration of stability for certain wave solutions via simulations.

Characterization of wave properties using quasi-continuous and numerical approaches.

Abstract

We study waves in a chain of dispersively coupled phase oscillators. Two approaches -- a quasi-continuous approximation and an iterative numerical solution of the lattice equation -- allow us to characterize different types of traveling waves: compactons, kovatons, solitary waves with exponential tails as well as a novel type of semi-compact waves that are compact from one side. Stability of these waves is studied using numerical simulations of the initial value problem.