Breather waves, high-order rogue waves and their dynamics in the coupled nonlinear Schrödinger equations with alternate signs of nonlinearities

School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology Xuzhou 221116, PRC

^(a) shoufu2006@126.com, sftian@cumt.edu.cn (corresponding author)

Received: 12 July 2019
Accepted: 22 August 2019

Abstract

We consider the analytic vector breather and high-order rogue wave solutions for the coupled nonlinear Schrödinger (NLS) equations with alternate signs of nonlinearities via Darboux dressing transformation. By adjusting spectral parameters, we indicate that the breather wave solutions contain temporally periodic nonlinear waves and spatially periodic nonlinear waves, respectively. The vector rogue wave solutions include the bright one-peak-two-valleys rogue wave and the bright rogue wave without valleys. Additionally, we successfully show different types of the distributions for the second-order vector rogue waves. The existence condition for the rogue waves is discussed. For the coupled NLS equations with alternate signs of nonlinearities, the rogue wave solutions exist if the baseband modulation instability (MI) is present.