Asymptotic behaviour of non-radiative solution to the wave equations

TL;DR

This paper characterizes weakly non-radiative solutions to linear and nonlinear wave equations, showing that in three dimensions, their initial data resemble those of free waves asymptotically, advancing understanding of wave behavior.

Contribution

It provides a comprehensive characterization of weakly non-radiative solutions without radial assumptions and links nonlinear solutions to free wave asymptotics in three dimensions.

Findings

All weakly non-radiative free waves characterized

Initial data of nonlinear non-radiative solutions resemble free waves asymptotically in 3D

Extends understanding of wave non-radiative behavior beyond radial symmetry

Abstract

In this work we consider weakly non-radiative solutions to both linear and non-linear wave equations. We first characterize all weakly non-radiative free waves, without the radial assumption. Then in dimension 3 we show that the initial data of non-radiative solutions to a wide range of nonlinear wave equations are similar to those of non-radiative free waves in term of asymptotic behaviour.