Dynamics of superregular breathers in the quintic nonlinear Schrödinger equation

In this paper, we consider an extended nonlinear Schrödinger equation that includes fifth-order dispersion with matching higher-order nonlinear terms. Via the modified Darboux transformation and Joukowsky transform, we present the superregular breather (SRB), multipeak soliton and hybrid solutions....

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Bibliographic Details
Published in:Nonlinear dynamics 2018-10, Vol.94 (2), p.977-989
Main Authors: Wang, Lei, Liu, Chong, Wu, Xuan, Wang, Xin, Sun, Wen-Rong
Format: Article
Language:English
Subjects:
Automotive Engineering
Breathers
Classical Mechanics
Control
Corresponding states
Dynamic stability
Dynamical Systems
Engineering
Exact solutions
Experiments
Laboratories
Mechanical Engineering
Nonlinear dynamics
Optics
Original Paper
Partial differential equations
Perturbation
Physics
Propagation
Schrodinger equation
Solitary waves
Stability analysis
Vibration
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Summary:In this paper, we consider an extended nonlinear Schrödinger equation that includes fifth-order dispersion with matching higher-order nonlinear terms. Via the modified Darboux transformation and Joukowsky transform, we present the superregular breather (SRB), multipeak soliton and hybrid solutions. The latter two modes appear as a result of the higher-order effects and are converted from a SRB one, which cannot exist for the standard NLS equation. These solutions reduce to a small localized perturbation of the background at time zero, which is different from the previous analytical solutions. The corresponding state transition conditions are given analytically. The relationship between modulation instability and state transition is unveiled. Our results will enrich the dynamics of nonlinear waves in a higher-order wave system.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4404-x