Large time asymptotics of solutions to the short-pulse equation

TL;DR

This paper investigates the long-term behavior of solutions to the short-pulse equation, establishing global existence and modified scattering for small initial data using wave packet methods.

Contribution

It introduces a novel application of wave packet testing to analyze the large-time asymptotics of the short-pulse equation.

Findings

Proves small data global existence.

Establishes modified scattering behavior.

Demonstrates effectiveness of wave packet method.

Abstract

We consider the long-time behavior of solutions to the short-pulse equation. Using the method of testing by wave packets, we prove small data global existence and modified scattering.