Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects

In this paper, we study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with fourth-order effects describing an inhomogeneous one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or alpha helical protein. The first-order nonautonomous breather solution of the four...

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Bibliographic Details
Published in:Nonlinear dynamics 2017-11, Vol.90 (3), p.2221-2230
Main Authors: Cai, Liu-Ying, Wang, Xin, Wang, Lei, Li, Min, Liu, Yong, Shi, Yu-Ying
Format: Article
Language:English
Subjects:
Alpha iron
Automotive Engineering
Classical Mechanics
Coefficients
Control
Dispersion
Dynamical Systems
Engineering
Ferromagnetism
Group velocity
Management systems
Mechanical Engineering
Modulation
Original Paper
Propagation
Proteins
Schrodinger equation
Solitary waves
Stability
Stability analysis
Vibration
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Summary:In this paper, we study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with fourth-order effects describing an inhomogeneous one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or alpha helical protein. The first-order nonautonomous breather solution of the fourth-order vc-NLS equation is derived. The state transition between nonautonomous breather and nonautonomous multi-peak soliton can be realized when group velocity dispersion (GVD) coefficient is proportional to the fourth-order dispersion (FOD) coefficient. We also display how the higher-order effects influence the nonautonomous multi-peak solitons. Our results show that the velocity and localization of the nonautonomous multi-peak soliton are affected by the FOD coefficient, and the peak number is controlled by the GVD coefficient. Further, we also show the compression effect and motion with variable velocity of nonautonomous multi-peak soliton in two kinds of dispersion management systems. Finally, we reveal the relation between the state transition and the modulation instability (MI) analysis.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3797-2