Eur. Phys. J. D (2012) 66: 112
https://doi.org/10.1140/epjd/e2012-20718-0

Regular Article

Controllable rogue waves in the nonautonomous nonlinear system with a linear potential

¹ School of Sciences, Zhejiang A&F University, Lin’an, Zhejiang 311300, P.R. China
² School of Physical Science and Technology, Suzhou University, Suzhou, Jiangsu 215006, P.R. China
³ College of Physics and Electromechanical Engineering, Shaoguan University, Guangdong 512005, P.R. China
⁴ School of Science, Zhejiang Lishui University, Lishui, Zhejiang 323000, P.R. China

^a e-mail: dcq424@126.com

Received: 9 December 2011
Received in final form: 13 February 2012
Published online: 30 April 2012

Abstract

Based on the similarity transformation connected the nonautonomous nonlinear Schrödinger equation with the autonomous nonlinear Schrödinger equation, we firstly derive self-similar rogue wave solutions (rational solutions) for the nonautonomous nonlinear system with a linear potential. Then, we investigate the controllable behaviors of one-rogue wave, two-rogue wave and rogue wave triplets in a soliton control system. Our results demonstrate that the propagation behaviors of rogue waves, including postpone, sustainment, recurrence and annihilation, can be manipulated by choosing the relation between the maximum value of the effective propagation distance Z_m and the parameter Z₀. Moreover, the excitation time of controllable rogue waves is decided by the parameter T₀.