Lump type solutions: Bäcklund transformation and spectral properties

Abstract

There are various different ways to obtain traveling waves of lump type(higher order lumps) for the KP-I equation. We propose a general and simple approach to derive them via a Bäcklund transformation. This enables us to establish an explicit connection between those lower energy solutions and higher energy ones. Based on this construction, spectral analysis of the degree 6 solutions is then carried out in details. The analysis of higher energy ones can be done in an inductive way.