Eur. Phys. J. E (2019) 42: 5
https://doi.org/10.1140/epje/i2019-11764-4

Regular Article

Possibility of the existence of the rogue wave and the super rogue wave in granular matter

¹ College of Physics and Electronic Engineering, Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China
² Joint Laboratory of Atomic and Molecular Physics of NWNU &IMP CAS, Northwest Normal University, 730070, Lanzhou, China

^* e-mail: liangtao0623@126.com
^** e-mail: duanws@nwnu.edu.cn

Received: 20 September 2018
Accepted: 10 December 2018
Published online: 17 January 2019

Abstract

By using the traditional perturbation technique, a focusing nonlinear Schrödinger equation (NLSE) for the one-dimensional bead chain with the initial prestress is first obtained. The Peregrine soliton, called the rogue wave in the present paper, and the super rogue wave are investigated both numerically and analytically. It is noted that both the rogue wave and the super rogue wave do exist in the one-dimensional bead chain. The solutions from the NLSE can correctly describe the real rogue wave as well as the real super rogue wave in the limiting case of small amplitude. Both the rogue wave and the super rogue wave propagate in the granular bead chain as if they are solitary waves.