The effect of coherent coupling nonlinearity on modulation instability and rogue wave excitation

AbstractIn this article, a fifth-order nonlinear Schrödinger equation, which can be used to characterise the solitons in the optical fibre and inhomogeneous Heisenberg ferromagnetic spin system, has been investigated. Akhmediev breather, Kuzentsov soliton, and generalised soliton have all been attained via the Darbox transformation. Propagation and interaction for three-type breathers have been studied: the types of breather are determined by the module and complex angle of parameter ξ; interaction between Akhmediev breather and generalised soliton displays a phase shift, whereas the others do not. Modulation instability of the generalised solitons have been analysed: a small perturbation can develop into a rogue wave, which is consistent with the results of rogue wave solutions.

Download Full-text

Optical Rogue Wave Excitation and Modulation on a Bright Soliton Background

Chinese Physics Letters ◽

10.1088/0256-307x/33/1/010501 ◽

2016 ◽

Vol 33 (1) ◽

pp. 010501 ◽

Cited By ~ 6

Author(s):

Liang Duan ◽

Zhan-Ying Yang ◽

Chong Liu ◽

Wen-Li Yang

Keyword(s):

Rogue Wave ◽

Bright Soliton ◽

Wave Excitation

Download Full-text

Dynamics of rogue wave excitation pattern on stripe phase backgrounds in a two-component Bose-Einstein condensate

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2017.02.004 ◽

2017 ◽

Vol 49 ◽

pp. 39-47 ◽

Cited By ~ 8

Author(s):

Li-Chen Zhao ◽

Liming Ling ◽

Jian-Wen Qi ◽

Zhan-Ying Yang ◽

Wen-Li Yang

Keyword(s):

Rogue Wave ◽

Einstein Condensate ◽

Wave Excitation ◽

Stripe Phase ◽

Bose Einstein Condensate ◽

Two Component ◽

Excitation Pattern ◽

Bose Einstein

Download Full-text

Rogue waves of ultra-high peak amplitude: a mechanism for reaching up to a thousand times the background level

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2020.0842 ◽

2021 ◽

Vol 477 (2246) ◽

pp. 20200842

Author(s):

Wen-Rong Sun ◽

Lei Liu ◽

P. G. Kevrekidis

Keyword(s):

Rogue Wave ◽

Background Level ◽

Rogue Waves ◽

Background Field ◽

High Peak ◽

Peak Amplitude ◽

Rational Solutions ◽

Fourth Degree ◽

Coupled Equations ◽

Coherent Coupling

We unveil a mechanism enabling a fundamental rogue wave, expressed by a rational function of fourth degree, to reach a peak amplitude as high as a thousand times the background level in a system of coupled nonlinear Schrödinger equations involving both incoherent and coherent coupling terms with suitable coefficients. We obtain the exact explicit vector rational solutions using a Darboux-dressing transformation. We show that both components of such coupled equations can reach extremely high amplitudes. The mechanism is confirmed in direct numerical simulations and its robustness is confirmed upon noisy perturbations. Additionally, we showcase the fact that extremely high peak-amplitude vector fundamental rogue waves (of about 80 times the background level) can be excited even within a chaotic background field .

Download Full-text

Multi-rogue Wave Solutions for a Generalized Integrable Discrete Nonlinear Schrodinger Equation With Higher-order Excitations

10.21203/rs.3.rs-350865/v1 ◽

2021 ◽

Author(s):

Ma Li-Yuan ◽

Yang Jun ◽

Zhang Yan-Li

Keyword(s):

Modulation Instability ◽

Rogue Wave ◽

Order Term ◽

Higher Order ◽

Discrete Version ◽

Nls Equation ◽

Third Order ◽

Discrete Nonlinear Schrödinger Equation ◽

Dynamical Behaviors ◽

Continuous Waves

Abstract In this paper, we construct the discrete rogue wave(RW) solutions for a higher-order or generalized integrable discrete nonlinear Schr¨odinger(NLS) equation. First, based on the modified Lax pair, the discrete version of generalized Darboux transformation are constructed. Second, the dynamical behaviors of first-, second- and third-order RWsolutions are investigated in corresponding to the unique spectral parameter λ, higher-order term coefficient γ, and free constants dk, fk (k = 1, 2, · · · ,N), which exhibit affluent wave structures. The differences between the RW solution of the higher-order discrete NLS equation and that of the Ablowitz-Ladik(AL) equation are illustrated in figures. Moreover, numerical experiments are explored, which demonstrates that strong-interaction RWs are stabler than the weak-interaction RWs. Finally, the modulation instability of continuous waves is studied.

Download Full-text