Dynamics and bifurcations of travelling wave solutions of R(<Emphasis Type="Italic">m,n</Emphasis>) equations |
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Authors: | Dahe Feng Jibin Li |
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Institution: | (1) School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, People’s Republic of China;(2) Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, People’s Republic of China |
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Abstract: | By using the bifurcation theory and methods of planar dynamical systems to R(m, n) equations, the dynamical behavior of different physical structures like smooth and non-smooth solitary wave, kink wave,
smooth and non-smooth periodic wave, and breaking wave is obtained. The qualitative change in the physical structures of these
waves is shown to depend on the systemic parameters. Under different regions of parametric spaces, various sufficient conditions
to guarantee the existence of the above waves are given. Moreover, some explicit exact parametric representations of travelling
wave solutions are listed. |
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Keywords: | R(m n) equations solitary wave periodic wave breaking wave solitary cusp wave periodic cusp wave |
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