Vector solitons and rogue waves of the matrix Lakshmanan-Porsezian-Daniel equation

With the Darboux-dressing transformation, we study the vector solitons and rogue waves of the matrix Lakshmanan-Porsezian-Daniel equation. Firstly, we show the dynamics of vector bright solitons with the higher-order effects. To be specific, one component of the vector solitons has one hump, while another one has two humps. Secondly, we show the fundamental vector rogue waves of ultra-high peak amplitudes on the constant backgrounds with the higher-order effects. Besides, the link between the baseband modulation instability and rogue waves is confirmed.