Cauchy matrix approach to integrable equations with self-consistent sources and the Yajima–Oikawa system

Abstract

A new approach by means of the Cauchy matrix is developed to obtain integrable equations with self-consistent sources. We derive a lower order Kadomtsev–Petviashvili equation with self-consistent sources which is then reduced to the multi-component Yajima–Oikawa system. This approach allows explicit multiple-pole solutions. New solutions of the Yajima–Oikawa system are obtained, of which there is more freedom in dispersion relations and amplitudes.