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.

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.

Higher-order Effects to the Transmission of Rogue Wave

2014 ◽  
Vol 20 (2) ◽  
pp. 143-147
Author(s):  
李淑青 LI Shu-qing ◽  
杨光晔 YANG Guang-ye ◽  
李禄 LI Lu
Keyword(s):  
Rogue Wave ◽  
Higher Order ◽  
Order Effects ◽  
Higher Order Effects

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

Higher-Order Approximations for Darcian Free Convective Flow About a Semi-Infinite Vertical Flat Plate

1984 ◽  
Vol 106 (1) ◽  
pp. 143-151 ◽  
Author(s):  
P. Cheng ◽  
C. T. Hsu
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Order Term ◽  
Leading Edge ◽  
Higher Order ◽  
Order Effects ◽  
Third Order ◽  
Higher Order Effects ◽  
Vertical Flat Plate

Higher-order effects of Darcian free convection boundary-layer flow adjacent to a semi-infinite vertical flat plate with a power law variation of wall temperature (i.e., Tˆw αxˆλ for xˆ≥0) are examined theoretically in this paper. The method of matched asymptotic expansions is used to construct inner and outer expansions. The small parameter of the perturbation series is the inverse of the square root of the Rayleigh number. The leading term in the inner expansions is taken to be the boundary layer theory with the second-order term due to the entrainment effect, and the third-order term due to the transverse pressure gradient and the streamwise heat conduction. The ordering of the term due to the leading edge effect depends on the wall temperature distribution; this term is determinate within a multiplicative constant owing to the appearance of an eigenfunction in the inner expansion. Thus, the perturbation solutions are carried out up to this term. For the case of an isothermal vertical plate (λ = 0), the second-order corrections for both the Nusselt number and the vertical velocity are zero, with the leading edge effect appearing in the third-order term. For λ>0, both the second- and third-order corrections in the Nusselt number are positive. The increase in surface heat flux is due to the fact that the higher-order effects increase the velocity parallel to the heated surface. The boundary layer theory for the prediction of the Nusselt number is shown to be quite accurate even at small Rayleigh number for 0≤λ≤1/3. The higher order effects tend to have a stronger influence on the velocity distribution than the temperature distribution. These effects become more pronounced as λ is increased from λ=1/3, or as the Rayleigh number is decreased.

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