Rogue wave patterns and hybrid solutions of rogue wave and breather for the Yajima-Oikawa-Newell system

Abstract For the Yajima-Oikawa-Newell (YON) system, we show that the rogue waves in the short-wave component exhibit three states: dark state, intermediate state and bright state, whereas the rogue waves in the long-wave component show only a dark state, or only a bright state, or both dark state and bright state depending on values of α , δ . We establish a connection between the N -th order rogue wave patterns for the YON system and the root structures of the Adler-Moser polynomials. We demonstrate that the rogue wave patterns result from a combination of operations including rotation, stretch, shear and a constant phase shift to the root structures of the Adler-Moser polynomials. We present the predicted fourth and fifth-order rogue wave patterns in the short-wave component for the dark state, intermediate state and bright state, which achieve excellent agreement with the corresponding true rogue wave patterns. Moreover, through a generalized long-wave limit method, we derive the hybrid solutions of rogue wave and breather for the YON system from its breather solutions. Each hybrid solution contains all free parameters from the individual rogue wave and breather involved in this hybrid solution. By managing the phase parameters of the breathers, we illustrate diverse interaction phenomena between breathers and rogue waves.