The Cauchy problem of the Ward equation with mixed scattering data

TL;DR

This paper addresses solving the Ward equation's Cauchy problem by incorporating both continuous and discrete scattering data, advancing the understanding of its integrable structure.

Contribution

It introduces a method to solve the Ward equation's Cauchy problem with mixed scattering data, combining continuous and discrete components.

Findings

Successfully solved the Cauchy problem with mixed scattering data

Extended the inverse scattering transform to handle combined data types

Provided a framework for analyzing solutions with mixed spectral data

Abstract

We solve the Cauchy problem of the Ward equation with both continuous and discrete scattering data.