Long waves in oceanic shallow water: Symbolic computation on the bilinear forms and Bäcklund transformations for the Whitham–Broer–Kaup system

Gao, Xin-Yi; Guo, Yong-Jiang; Shan, Wen-Rui

doi:10.1140/epjp/s13360-020-00592-5

Cited by 20 publications

(1 citation statement)

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“…which can be applied in the internal solitray wave dynamics, but also can be used to describe the propagation of the weakly nonlinear waves in a composite medium. [13] Many effective methods have been proposed to analyze partial differential equations, such as Painlevé analysis, [14][15][16] symmetry group, [17][18][19] consistent Riccati expansion (CRE), [20][21][22] and so on. [23,24] To our knowledge, the CRE solvability, symmetries and cnoidal-solitary wave interaction solutions of the forced variable-coefficient extended KdV equation have not been studied.…”

Section: Introductionmentioning

confidence: 99%

Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg–de Vries equation in fluid dynamics of internal solitary waves*

Liu¹,

Huang²,

Ren³

et al. 2021

Chinese Phys. B

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We study a forced variable-coefficient extended Korteweg–de Vries (KdV) equation in fluid dynamics with respect to internal solitary wave. Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated Painlevé expansion. When the variable coefficients are time-periodic, the wave function evolves periodically over time. Symmetry calculation shows that the forced variable-coefficient extended KdV equation is invariant under the Galilean transformations and the scaling transformations. One-parameter group transformations and one-parameter subgroup invariant solutions are presented. Cnoidal wave solutions and solitary wave solutions of the forced variable-coefficient extended KdV equation are obtained by means of function expansion method. The consistent Riccati expansion (CRE) solvability of the forced variable-coefficient extended KdV equation is proved by means of CRE. Interaction phenomenon between cnoidal waves and solitary waves can be observed. Besides, the interaction waveform changes with the parameters. When the variable parameters are functions of time, the interaction waveform will be not regular and smooth.

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