## Taiwanese Journal of Mathematics

### Quasi-periodic Waves and Solitary Waves to a Generalized KdV-Caudrey-Dodd-Gibbon Equation from Fluid Dynamics

#### Abstract

In this paper, a generalized KdV-Caudrey-Dodd-Gibbon (KdV-CDG) equation is investigated, which describes certain situations in the fluid mechanics, ocean dynamics and plasma physics. By using Bell polynomials, a lucid and systematic approach is proposed to systematically study its Hirota's bilinear form and $N$-soliton solution, respectively. Furthermore, based on the Riemann theta function, the one-quasi- and two-quasi-periodic wave solutions are also constructed. Finally, an asymptotic relation of the quasi-periodic wave solutions are strictly analyzed to reveal the relations between quasi-periodic wave solutions and soliton solutions.

#### Article information

Source
Taiwanese J. Math., Volume 20, Number 4 (2016), 823-848.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874493

Digital Object Identifier
doi:10.11650/tjm.20.2016.6850

Mathematical Reviews number (MathSciNet)
MR3535676

Zentralblatt MATH identifier
1357.35256

#### Citation

Tu, Jian-Min; Tian, Shou-Fu; Xu, Mei-Juan; Zhang, Tian-Tian. Quasi-periodic Waves and Solitary Waves to a Generalized KdV-Caudrey-Dodd-Gibbon Equation from Fluid Dynamics. Taiwanese J. Math. 20 (2016), no. 4, 823--848. doi:10.11650/tjm.20.2016.6850. https://projecteuclid.org/euclid.twjm/1498874493

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