Open Access
2016 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, Tian-Tian Zhang
Taiwanese J. Math. 20(4): 823-848 (2016). DOI: 10.11650/tjm.20.2016.6850
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.

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Copyright © 2016 The Mathematical Society of the Republic of China
Jian-Min Tu, Shou-Fu Tian, Mei-Juan Xu, and Tian-Tian Zhang "Quasi-periodic Waves and Solitary Waves to a Generalized KdV-Caudrey-Dodd-Gibbon Equation from Fluid Dynamics," Taiwanese Journal of Mathematics 20(4), 823-848, (2016). https://doi.org/10.11650/tjm.20.2016.6850
Published: 2016
Vol.20 • No. 4 • 2016
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