Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System
Year: 2021
Author: Ronghua Cheng, Zhaofu Luo, Xiaochun Hong
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 2 : pp. 193–207
Abstract
In this paper, we employ the theory of the planar dynamical system to investigate the dynamical behavior and bifurcations of solutions of the traveling systems of the $D(m,n)$ equation. On the basis of the previous work of the reference [17], we obtain the solitary cusp waves solutions (peakons and valleyons), breaking wave solutions (compactons) and other periodic cusp wave solutions. Morever, we make a summary of exact traveling wave solutions to the $D(m,n)$ system including all the solutions which have been found from the references [4, 14, 17].
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2021.193
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 2 : pp. 193–207
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: $D(m n)$ system Solitary wave solution Periodic wave solution Compacton Peakon.