Study of the generalization of regularized long-wave equation

A generalization of the regularized long-wave equation is considered, and the existences of smooth soliton, peakon, and periodic solutions are established via the complete discrimination system for polynomial method and the bifurcation method. Concrete examples of these solutions are constructed to...

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Bibliographic Details
Published in:Nonlinear dynamics 2022-02, Vol.107 (3), p.2745-2752
Main Authors: Kai, Yue, Ji, Jialiang, Yin, Zhixiang
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Mechanical Engineering
Original Paper
Partial differential equations
Physics
Polynomials
Solitary waves
Vibration
Water waves
Wave equations
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Summary:A generalization of the regularized long-wave equation is considered, and the existences of smooth soliton, peakon, and periodic solutions are established via the complete discrimination system for polynomial method and the bifurcation method. Concrete examples of these solutions are constructed to verify our conclusions directly. In particular, we construct a special kind of smooth soliton solution, namely a Gaussian soliton solution, and give two sufficient conditions for the existence of such a solution by the extended trial equation method. To the best of our knowledge, this is the first time that a Gaussian soliton solution has been constructed for an equation with no logarithmic nonlinearity.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-021-07115-6