Lump type solutions: Backlund transformation and spectral properties

2023/12/02 by Liu, Yong, Wei, Jun-cheng, Yang, Wen · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.01063

Abstract

There are various different ways to obtain traveling waves of lump type for the KP equation. We propose a general and simple approach to derive them via a Backlund transformation. This enables us to establish an explicit connection between those low energy solutions and high 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.

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