https://doi.org/10.1140/epjp/i2016-16241-1
Regular Article
On periodic wave solutions and asymptotic behaviors to a generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation
1
Department of Mathematics, China University of Mining and Technology, 221116, Xuzhou, China
2
Center of Nonlinear Equations, China University of Mining and Technology, 221116, Xuzhou, China
* e-mail: sftian@cumt.edu.cn
Received:
16
March
2016
Accepted:
21
June
2016
Published online:
25
July
2016
In this paper, a lucid and systematic approach is proposed to systematically study the periodic-wave solutions and asymptotic behaviors of a (2 + 1) -dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. Based on Bell's polynomials, the bilinear formalism and N -soliton solution of the gKDKK equation are derived, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic-wave solutions of the equation are also constructed. Finally, an asymptotic relation between the periodic-wave solutions and soliton solutions are strictly established under a limited procedure.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016
