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

• 作者: Ping Liu Bing Huang Bo Ren Jian-Rong Yang
• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2021,（8）
• 所属期刊栏目: GENERAL
• 页码范围: 222-230
• 页数: 9页
• 语种: 英文
• DOI: 10.1088/1674-1056/ac052a

摘要

We study a forced variable-coefficient extended Korteweg-de Vries (KdV) equation in fluid dynamics with respect to intemal solitary wave.B(a)cklund transformations of the forced variable-coefficient extended KdV equation are demon-strated 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.Interac-tion 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.