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

被引：56

作者：

Chen, Jinbing ^{[1
]}

Pelinovsky, Dmitry E. ^{[2
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China

[2] McMaster Univ, Dept Math, Hamilton, ON L8S 4K1, Canada

来源：

PHYSICAL REVIEW E | 2021年 / 103卷 / 06期

基金：

中国国家自然科学基金;

关键词：

MODULATIONAL INSTABILITY; NLS;

D O I：

10.1103/PhysRevE.103.062206

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

The derivative nonlinear Schrodinger (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.

引用

页数：25

共 40 条

[1] Integrable turbulence generated from modulational instability of cnoidal waves [J].

Agafontsev, D. S. ;

Zakharov, V. E. .

NONLINEARITY, 2016, 29 (11) :3551-3578

[2] Rogue waves and rational solutions of the nonlinear Schroumldinger equation [J].

Akhmediev, Nail ;

Ankiewicz, Adrian ;

Soto-Crespo, J. M. .

PHYSICAL REVIEW E, 2009, 80 (02)

[3] Baseband modulation instability as the origin of rogue waves [J].

Baronio, Fabio ;

Chen, Shihua ;

Grelu, Philippe ;

Wabnitz, Stefan ;

Conforti, Matteo .

PHYSICAL REVIEW A, 2015, 91 (03)

[4] Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime [J].

Baronio, Fabio ;

Conforti, Matteo ;

Degasperis, Antonio ;

Lombardo, Sara ;

Onorato, Miguel ;

Wabnitz, Stefan .

PHYSICAL REVIEW LETTERS, 2014, 113 (03)

[5]

Bronski JC, 2016, LECT NOTES PHYS, V908, P83, DOI 10.1007/978-3-319-20690-5_4

[6] A (2+1)-dimensional derivative Toda equation in the context of the Kaup-Newell spectral problem [J].

Cao, Cewen ;

Yang, Xiao .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (02)

[7] Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation [J].

Chen, Jinbing ;

Pelinovsky, Dmitry E. ;

Upsal, Jeremy .

JOURNAL OF NONLINEAR SCIENCE, 2021, 31 (03)

[8] The complex Hamiltonian systems and quasi-periodic solutions in the derivative nonlinear Schrodinger equations [J].

Chen, Jinbing ;

Zhang, Runsu .

STUDIES IN APPLIED MATHEMATICS, 2020, 145 (02) :153-178

[9] Periodic standing waves in the focusing nonlinear Schrodinger equation: Rogue waves and modulation instability [J].

Chen, Jinbing ;

Pelinovsky, Dmitry E. ;

White, Robert E. .

PHYSICA D-NONLINEAR PHENOMENA, 2020, 405

[10] Periodic Travelling Waves of the Modified KdV Equation and Rogue Waves on the Periodic Background [J].

Chen, Jinbing ;

Pelinovsky, Dmitry E. .

JOURNAL OF NONLINEAR SCIENCE, 2019, 29 (06) :2797-2843

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