Doubly localized rogue waves on a background of dark solitons for the Fokas system

• DOI: 10.1016/j.aml.2021.107435
• Publication Date: 2021-05-31T15:54:15Z
• Authors: Jiguang Rao; Jingsong He; Dumitru Mihalache
• Keywords: 0103 physical sciences; 01 natural sciences

Abstract Under investigation in this letter are the two-dimensional doubly localized rogue waves on a background of dark solitons for the Fokas system, which are described by semi-rational solutions. There are two types of doubly localized rogue waves: the line segment rogue waves and the lump-type ones. The line segment rogue waves arise and decay on the background of dark solitons with line segment profiles of finite length. The lump-type rogue waves appear from and disappear into dark solitons in the form of lumps. Both the line segment rogue waves and lump-type ones are truly localized in two-dimensional space and in time. These doubly localized rogue waves are an extension of the reported rogue waves in two-dimensional systems, and have great importance in nonlinear science and physical applications.