Deformed breather and rogue waves for the inhomogeneous fourth-order nonlinear Schrödinger equation in alpha-helical proteins

The inhomogeneous fourth-order nonlinear Schrödinger equation is investigated, which models the transport of energy along the inhomogeneous hydrogen bonding spines in alpha-helical proteins. The deformed breather and rogue waves solutions for the equation are derived via Darboux transformation. Ther...

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Bibliographic Details
Published in:Nonlinear dynamics 2020-05, Vol.100 (3), p.2779-2795
Main Authors: Meng, Gao-Qing, Pan, Yu-Song, Xie, Xi-Yang
Format: Article
Language:English
Subjects:
Automotive Engineering
Breathers
Classical Mechanics
Coefficient of variation
Control
Deformation
Dynamical Systems
Energy
Engineering
Hydrogen bonding
Inhomogeneity
Mechanical Engineering
Original Paper
Peptides
Proteins
Pulse duration
Schrodinger equation
Vibration
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Summary:The inhomogeneous fourth-order nonlinear Schrödinger equation is investigated, which models the transport of energy along the inhomogeneous hydrogen bonding spines in alpha-helical proteins. The deformed breather and rogue waves solutions for the equation are derived via Darboux transformation. Thereinto, the modified limit procedure in generalized Darboux transformation is proposed to construct the expressions of higher-order rogue waves. Due to the presence of inhomogeneity, despite their diversity profiles, the shape, amplitude and pulse width of each deformed breather will change with time. When the coefficients of higher-order terms are varied, the propagating trajectories of breathers are changed. Head-on collision, partially coalesced, without interaction between two deformed breathers is found under diverse selected parameters. The temporal-spatial structures of the presented rogue waves exhibit certain valleys around one or several centers, and the peak heights of those rogue waves are more than three times that of the background. Additionally, the distributed area of the rogue wave will tend to be broaden/narrow along the temporal axis, with the variation of the coefficients of inhomogeneity and higher-order terms.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-05622-6