Higher-order interactional solutions and rogue wave pairs for the coupled Lakshmanan–Porsezian–Daniel equations

Abstract

The N-fold Darboux transformation of the coupled Lakshmanan–Porsezian–Daniel (LPD) equations is constructed. Based on the Darboux transformation and the limiting technique, we investigate two kinds of solutions for the coupled LPD equations, which are higher-order interactional solutions and rogue wave (RW) pairs. Through considering the double-root situation of the spectral characteristic equation for the matrix in the Lax pair, we give the higher-order interactional solutions among higher-order RWs, multi-bright (dark) solitons and multi-breather. Besides, we consider the triple-root situation of the spectral characteristic equation and get the higher-order RW pairs. It demonstrates that the RW pairs are greatly different form the traditional higher-order RWs. The fist-order RW pairs can split into two traditional first-order RWs, and four or six traditional fundamental RWs can emerge from the second-order case. The corresponding dynamics of these explicit solutions are discussed in detail.