Mixed localized waves and their dynamics for a matrix Lakshmanan–Porsezian–Daniel equation

Abstract

Interactions between different localized waves are of great significance to physical systems. In this paper, we study the mixed localized waves and their dynamics based on the matrix Lakshmanan–Porsezian–Daniel equation. First, we construct the Nth-order mixed localized solutions describing the interactions between the (N−1) th-order rogue waves and breathers. Using these solutions, we discuss the second- and third-order mixed localized waves, as well as their dynamics. Furthermore, we describe five types of interactions between rogue waves and breathers: between the first-order rogue waves and temporal period breathers, the first-order rogue waves and spatial period breathers, the first-order rogue waves and spatial-temporal period breathers, the second-order rogue waves and temporal period breathers, and the second-order rogue waves and spatial period breathers. These results may be useful for the study of nonlinear wave interactions in physical systems.