TY - JOUR
T1 - Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System
AU - Cheng , Ronghua
AU - Luo , Zhaofu
AU - Hong , Xiaochun
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 193
EP - 207
PY - 2021
DA - 2021/04
SN - 3
DO - http://doi.org/10.12150/jnma.2021.193
UR - https://global-sci.org/intro/article_detail/jnma/18786.html
KW - $D(m, n)$ system, Solitary wave solution, Periodic wave solution,
Compacton, Peakon.
AB - <p style="text-align: justify;">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].</p>