A novel approach to a time-dependent-coefficient WBK system: doubly periodic waves and singular nonlinear dynamics
type: Item
instance of: scholarly article
title: A novel approach to a time-dependent-coefficient WBK system: doubly periodic waves and singular nonlinear dynamics
zbMATH Open document ID: 1405.35188
DOI: 10.1155/2018/3158126
author: Bo Xu
author: Sheng Zhang
published in: Complexity
publication date: 2018-12-18T00:00:00Z
review text: Summary: Under investigation in this paper is a more general time-dependent-coefficient Whitham-Broer-Kaup (tdcWBK) system, which includes some important models as special cases, such as the approximate equations for long water waves, the WBK equations in shallow water, the Boussinesq-Burgers equations, and the variant Boussinesq equations. To construct doubly periodic wave solutions, we extend the generalized \(F\)-expansion method for the first time to the tdcWBK system. As a result, many new Jacobi elliptic doubly periodic solutions are obtained; the limit forms of which are the hyperbolic function solutions and trigonometric function solutions. It is shown that the original \(F\)-expansion method cannot derive Jacobi elliptic doubly periodic solutions of the tdcWBK system, but the novel approach of this paper is valid. To gain more insight into the doubly periodic waves contained in the tdcWBK system, we simulate the dynamical evolutions of some obtained Jacobi elliptic doubly periodic solutions. The simulations show that the doubly periodic waves possess time-varying amplitudes and velocities as well as singularities in the process of propagations.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 6995123
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3158126
OpenAlex ID: W2889523101
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description: scientific article; zbMATH DE number 6995123