导数非线性薛定谔方程中周期驻波背景下的 rogue 波

Rogue waves on the background of periodic standing waves in the derivative nonlinear Schrödinger equation.

作者信息

Chen Jinbing, Pelinovsky Dmitry E

机构信息

School of Mathematics, Southeast University, Nanjing, Jiangsu 210096, People's Republic of China.

Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1.

出版信息

Phys Rev E. 2021 Jun;103(6-1):062206. doi: 10.1103/PhysRevE.103.062206.

DOI:10.1103/PhysRevE.103.062206

PMID:34271656

Abstract

The derivative nonlinear Schrödinger (DNLS) equation is the canonical model for the dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the DNLS equation. We show that the space-time localization of a rogue wave is only possible if the periodic standing wave is modulationally unstable. If the periodic standing wave is modulationally stable, the rogue wave solutions degenerate into algebraic solitons propagating along the background and interacting with the periodic standing waves. Maximal amplitudes of rogue waves are found analytically and confirmed numerically.

摘要

导数非线性薛定谔（DNLS）方程是等离子体物理和光学中非线性波动力学的典型模型。我们研究了描述DNLS方程中周期驻波背景下 rogue 波的精确解。我们表明，只有当周期驻波是调制不稳定时，rogue 波的时空局域化才有可能。如果周期驻波是调制稳定的，rogue 波解会退化为沿背景传播并与周期驻波相互作用的代数孤子。通过解析方法找到了 rogue 波的最大振幅，并通过数值方法得到了证实。