Taiwanese Journal of Mathematics

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

Jian-Min Tu, Shou-Fu Tian, Mei-Juan Xu, and Tian-Tian Zhang

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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

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

First available in Project Euclid: 1 July 2017

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Zentralblatt MATH identifier

Primary: 35Q51: Soliton-like equations [See also 37K40] 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35C99: None of the above, but in this section 68W30: Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10] 74J35: Solitary waves

generalized KdV-Caudrey-Dodd-Gibbon equation Hirota's bilinear method Riemann theta function soliton wave solution quasi-periodic wave solution


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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