Abstract
The theory of planar dynamical systems is used to study the dynamical behaviours of travelling wave solutions of a nonlinear wave equations of KdV type. In different regions of the parametric space, sufficient conditions to guarantee the existence of solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions are given. All possible exact explicit parametric representations are obtained for these waves.
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Contributed by LI Ji-bin
Project supported by the National Natural Science Foundation of China (No. 10231020), the Natural Science Foundation of Yunnan Province of China (No. 2003A0018M), and Key Project of the Science Foundation of Yunnan Education Department of China (No. 5Z0071A)
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Long, Y., Li, Jb., Rui, Wg. et al. Travelling wave solutions for a second order wave equation of KdV type. Appl. Math. Mech.-Engl. Ed. 28, 1455–1465 (2007). https://doi.org/10.1007/s10483-007-1105-y
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DOI: https://doi.org/10.1007/s10483-007-1105-y
Key words
- solitary wave solution
- periodic wave solution
- kink wave and anti-kink wave solutions
- smooth and non-smooth periodic waves