Appearing (disappearing) lumps and rogue lumps of the two-dimensional vector Yajima-Oikawa system

TL;DR

This paper constructs and generalizes various localized solutions, including lumps and rogue waves, for the two-dimensional multicomponent Yajima-Oikawa system using Darboux transformations, revealing new phenomena like appearing and disappearing lumps.

Contribution

It introduces novel generalizations of lump solutions, including appearing and disappearing lumps, for the two-dimensional multicomponent Yajima-Oikawa system.

Findings

Constructed solutions with functional arbitrariness using Darboux transformations.

Identified types of solutions including lumps, rogue waves, and semi-rational solutions.

Generalized lump solutions to include appearing and disappearing behaviors.

Abstract

The solutions of the two-dimensional multicomponent Yajima-Oikawa system that have the functional arbitrariness are constructed by using the Darboux transformation technique. For the zero and constant backgrounds, different types of solutions of this system, including the lumps, line rogue waves, semi-rational solutions and their higher-order counterparts, are considered. Also, the generalization of the lump solutions (namely, appearing or disappearing lumps) is obtained in the two-component case under the special choice of the arbitrary functions. Then, the suitable ansatz is used to find the further generalization of these lumps (appearing-disappearing lumps or rogue lumps).