Continuous limit and position adjustable rogue wave solutions for the semi-discrete complex coupled system associated with 4 × 4 Lax pair

Abstract

In this letter, we propose a new semi-discrete complex coupled system associated with 4 × 4 Lax pair. Firstly, the continuous limit technique is used to map this semi-discrete system to two new continuous complex equations. Then, the discrete generalized (m,N−m)-fold Darboux transformation for this system is first proposed. Finally, through applying the resulting Darboux transformation, some novel rogue wave and periodic wave structures with position adjustable parameters are investigated and discussed graphically. In particular, it is found that in the same semi-discrete system, the first-order rogue wave can have one or two fundamental rogue waves, and the second-order rogue wave can have three or six fundamental rogue waves.