Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System |
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| Authors: | Ronghua Cheng Zhaofu Luo Xiaochun Hong |
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| Affiliation: | 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 |
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| Abstract: | In this paper, we employ the theory of the planar dynamical systemto investigate the dynamical behavior and bifurcations of solutionsof the traveling systems of the $D(m,n)$ equation. On the basis ofthe previous work of the reference cite{zhang}, we obtain thesolitary cusp waves solutions (peakons and valleyons), breaking wavesolutions (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 foundfrom the references cite{Deng,Xie,zhang}. |
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| Keywords: | $D(m,n)$ system Solitary wave solution Periodic wave solution Compacton Peakon |
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