scholarly journals Strong and weak interactions of rational vector rogue waves and solitons to any n -component nonlinear Schrödinger system with higher-order effects

2022 ◽  
Vol 478 (2257) ◽  
Author(s):  
Weifang Weng ◽  
Guoqiang Zhang ◽  
Zhenya  Yan
Keyword(s):  
Fourth Order ◽  
Deep Ocean ◽  
Rogue Waves ◽  
Higher Order ◽  
Strong Interactions ◽  
Order Effects ◽  
Rational Solutions ◽  
Nonlinear Schrödinger ◽  
Rational Vector ◽  
Higher Order Effects

The higher-order effects play an important role in the wave propagations of ultrashort (e.g. subpicosecond or femtosecond) light pulses in optical fibres. In this paper, we investigate any n -component fourth-order nonlinear Schrödinger ( n -FONLS) system with non-zero backgrounds containing the n -Hirota equation and the n -Lakshmanan–Porsezian–Daniel equation. Based on the loop group theory, we find the multi-parameter family of novel rational vector rogue waves (RVRWs) of the n -FONLS equation starting from the plane-wave solutions. Moreover, we exhibit the weak and strong interactions of some representative RVRW structures. In particular, we also find that the W-shaped rational vector dark and bright solitons of the n -FONLS equation as the second- and fourth-order dispersion coefficients satisfy some relation. Furthermore, we find the higher-order RVRWs of the n -FONLS equation. These obtained rational solutions will be useful in the study of RVRW phenomena of multi-component nonlinear wave models in nonlinear optics, deep ocean and Bose–Einstein condensates.

Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein

2016 ◽  
Vol 71 (1) ◽  
pp. 27-32 ◽  
Author(s):  
Hui-Xian Jia ◽  
Yu-Jun Liu ◽  
Ya-Ning Wang
Keyword(s):  
Rogue Wave ◽  
Wave Interaction ◽  
Rogue Waves ◽  
Higher Order ◽  
Order Effects ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
Existence Time ◽  
Helical Protein ◽  
Higher Order Effects

AbstractIn this article, we investigate a fourth-order nonlinear Schrödinger equation, which governs the Davydov solitons in the alpha helical protein with higher-order effects. By virtue of the generalised Darboux transformation, higher-order rogue-wave solutions are derived. Propagation and interaction of the rogue waves are analysed: (i) Coefficients affect the existence time of the first-order rogue waves; (ii) coefficients affect the interaction time of the second- and third-order rogue waves; (iii) direction of the rogue-wave propagation remain unchanged after interaction.

Rogue waves in presence of higher order effects

2010 ◽  
Author(s):  
Nail Akhmediev ◽  
Adrian Ankiewicz ◽  
J. M. Soto-Crespo
Keyword(s):  
Rogue Waves ◽  
Higher Order ◽  
Order Effects ◽  
Higher Order Effects

Grey solitons and soliton interaction of higher nonlinear Schrödinger equation

2010 ◽  
Vol 88 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Qiu-Yan Li ◽  
Zai-Dong Li ◽  
Peng-Bin He ◽  
Wei-Wei Song ◽  
Guangsheng Fu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Continuous Wave ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Order Effects ◽  
Nonlinear Schrödinger ◽  
Grey Soliton ◽  
Higher Order Effects

In this paper, the higher nonlinear Schrödinger equation is solved by the Hirota method. As an example, the exact grey one- and two-soliton solutions in explicit forms are generated analytically under the continuous-wave background. The results reveal that the velocity of the grey soliton is clearly affected by the higher order effects, yet the grey soliton propagates without any change in their shape and intensity. The higher order term and the phase velocity play the important role for the maximum valley of grey soliton, i.e., the intensity of grey soliton. For the black soliton, the velocity of soliton is determined only by the higher order effects. The analysis of the asymptotic behavior of a two grey soliton solution shows the collision is elastic.

Time after time: support for memory accounts of temporal preparation.

2019 ◽  
Author(s):  
Joe Butler ◽  
Samuel Ngabo ◽  
Marcus Missal
Keyword(s):  
Response Times ◽  
Reaction Times ◽  
Evidence Base ◽  
Higher Order ◽  
Order Effects ◽  
Previous Trial ◽  
Adaptive Responses ◽  
Temporal Preparation ◽  
Subsequent Trial ◽  
Higher Order Effects

Complex biological systems build up temporal expectations to facilitate adaptive responses to environmental events, in order to minimise costs associated with incorrect responses, and maximise the benefits of correct responses. In the lab, this is clearly demonstrated in tasks which show faster response times when the period between warning (S1) and target stimulus (S2) on the previous trial was short and slower when the previous trial foreperiod was long. The mechanisms driving such higher order effects in temporal preparation paradigms are still under debate, with key theories proposing that either i) the foreperiod leads to automatic modulation of the arousal system which influences responses on the subsequent trial, or ii) that exposure to a foreperiod results in the creation of a memory trace which is used to guide responses on the subsequent trial. Here we provide data which extends the evidence base for the memory accounts, by showing that previous foreperiod exposures are cumulative with reaction times shortening after repeated exposures; whilst also demonstrate that the higher order effects associated with a foreperiod remain active for several trials.

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