Abstract
We present in this paper a generalised PC (GPC) equation which includes several known models. The corresponding traveling wave system is derived and we show that the homoclinic orbits of the traveling wave system correspond to the solitary waves of GPC equation, and the heteroclnic orbits correspond to the kink waves. Under some parameter conditions, the existence of above two types of orbits is demonstrated and the explicit expressions of the two solutions are worked out.
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Zhang, Wl. Solitary Wave Solutions and Kink Wave Solutions for a Generalized PC Equation. Acta Mathematicae Applicatae Sinica, English Series 21, 125–134 (2005). https://doi.org/10.1007/s10255-005-0223-1
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DOI: https://doi.org/10.1007/s10255-005-0223-1