Eur. Phys. J. Plus (2016) 131: 100
https://doi.org/10.1140/epjp/i2016-16100-1

Regular Article

Vector rogue waves in the mixed coupled nonlinear Schrödinger equations

¹ Department of Mathematics and Physics, North China Electric Power University, 102206, Beijing, China
² College of Science, China University of Petroleum, 102249, Beijing, China

^* e-mail: xutodd@126.com

Received: 4 October 2015
Accepted: 1 March 2016
Published online: 18 April 2016

Abstract

In this paper, via the generalized Darboux transformation we derive the reduced and non-reduced vector rogue wave solutions of the focusing-defocusing mixed coupled nonlinear Schrödinger equations. The dynamics of reduced vector rogue waves is the same as that for the known scalar ones. The non-reduced solutions can exhibit both the one-peak-two-valleys structure with one peak and two valleys lying in a straight line, and the two-peaks-two-valleys structure with two peaks and two valleys located at the four vertices of a parallelogram. We also find that the amplitude of the non-reduced vector rogue wave is not three times as that of the exciting plane wave, and that the coalescence of multiple fundamental rogue waves does not generate larger-amplitude rogue waves. In addition, we discuss the relationship of the free parameters in the solutions with the positions and relative distances of rogue waves in the xt-plane.