Dynamical analysis of position-controllable loop rogue wave and mixed interaction phenomena for the complex short pulse equation in optical fiber

This paper investigates the complex short pulse equation, which can govern the propagation of ultra-short pulse packets along optical fibers. From the known Lax pair of this equation, the generalized (n, N - n)-fold Darboux transformation is adopted to construct four types of position-controllable localized wave solutions, including loop rogue wave, loop semi-rational soliton, loop periodic wave and their mixed interaction structures, and graphical illustrations present these novel localized wave structures. It is shown that these localized wave solutions can become a loop shape due to hodograph transformation, which is different from other usual single-valued localized waves. Compared with the known results, the main highlight of this paper is not only to propose several new types of localized waves, but also to demonstrate how their positions can be controlled by particular parameters so that we can theoretically control them where we want them to appear; in particular, we derive some novel wave structures with diverse loop localized wave interaction phenomena. These exotic structures may enrich the understanding of the nature of loop rogue waves, which might help explain some physical phenomena in nonlinear optics.