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• W2889523101 abstract "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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi>F</mml:mi></mml:math>-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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>F</mml:mi></mml:math>-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." @default.
• W2889523101 created "2018-09-07" @default.
• W2889523101 creator A5025569041 @default.
• W2889523101 creator A5091521312 @default.
• W2889523101 date "2018-08-28" @default.
• W2889523101 modified "2023-10-18" @default.
• W2889523101 title "A Novel Approach to a Time-Dependent-Coefficient WBK System: Doubly Periodic Waves and Singular Nonlinear Dynamics" @default.
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• W2889523101 doi "https://doi.org/10.1155/2018/3158126" @default.
• W2889523101 hasPublicationYear "2018" @default.
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