The Cauchy Problem of the Ward equation

TL;DR

This paper extends the inverse scattering framework for the Ward equation to handle non-small data, solving the Cauchy problem with purely continuous scattering data, thus broadening the equation's solvability scope.

Contribution

It generalizes previous results to include non-small data and provides a solution to the Cauchy problem with purely continuous scattering data for the Ward equation.

Findings

Successfully solves the Cauchy problem with non-small continuous scattering data.

Extends inverse scattering methods to broader data regimes.

Builds on and generalizes prior theoretical frameworks.

Abstract

We generalize the results of Villarroel, Fokas and Ioannidou, Dai, Terng and Uhlenbeck to study the inverse scattering problem of the Ward equation with non-small data and solve the Cauchy problem of the Ward equation with a non-small purely continuous scattering data.