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| Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System |
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| KeyWord:$D(m,n)$ system Solitary wave solution Periodic wave solution Compacton Peakon |
| Author Name | Affiliation | | Ronghua Cheng | School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China
School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China | | Zhaofu Luo | School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China | | Xiaochun Hong | School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China |
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| 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 \cite{zhang}, 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 \cite{Deng,Xie,zhang}. |
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