On periodic wave solutions and asymptotic behaviors to a generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation
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
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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