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

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.

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.

scholarly journals Responsible innovation, anticipation and responsiveness: case studies of algorithms in decision support in justice and security, and an exploration of potential, unintended, undesirable, higher-order effects

AI and Ethics ◽  
2021 ◽  
Author(s):  
Marc Steen ◽  
Tjerk Timan ◽  
Ibo van de Poel
Keyword(s):  
Decision Support ◽  
Case Studies ◽  
Personal Data ◽  
Higher Order ◽  
Popular Media ◽  
Responsible Innovation ◽  
Order Effects ◽  
Key Dimensions ◽  
Higher Order Effects

AbstractThe collection and use of personal data on citizens in the design and deployment of algorithms in the domain of justice and security is a sensitive topic. Values like fairness, autonomy, privacy, accuracy, transparency and property are at stake. Negative examples of algorithms that propagate or exacerbate biases, inequalities or injustices have received ample attention, both in academia and in popular media. To supplement this view, we will discuss two positive examples of Responsible Innovation (RI): the design and deployment of algorithms in decision support, with good intentions and careful approaches. We then explore potential, unintended, undesirable, higher-order effects of algorithms—effects that may occur despite good intentions and careful approaches. We do that by engaging with anticipation and responsiveness, two key dimensions of Responsible Innovation. We close the paper with proposing a framework and a series of tentative recommendations to promote anticipation and responsiveness in the design and deployment of algorithms in decision support in the domain of justice and security.

Sign in / Sign up

Export Citation Format

Share Document