In this paper, we investigate the traveling wave solutions of a two-component Dullin–Gottwald–Holm (DGH) system. By qualitative analysis methods of planar systems, we investigate completely the topological behavior of the solutions of the traveling wave system, which is derived from the two-component Dullin–Gottwald–Holm system, and show the corresponding phase portraits. We prove the topological types of degenerate equilibria by the technique of desingularization. According to the dynamical behaviors of the solutions, we give all the bounded exact traveling wave solutions of the system, including solitary wave solutions, periodic wave solutions, cusp solitary wave solutions, periodic cusp wave solutions, compactonlike wave solutions, and kinklike and antikinklike wave solutions. Furthermore, to verify the correctness of our results, we simulate these bounded wave solutions using the software maple version 18.
Traveling Wave Solutions of a Two-Component Dullin–Gottwald–Holm System
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 4, 2016; final manuscript received October 18, 2016; published online December 5, 2016. Assoc. Editor: Firdaus Udwadia.
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Zhong, J., and Deng, S. (December 5, 2016). "Traveling Wave Solutions of a Two-Component Dullin–Gottwald–Holm System." ASME. J. Comput. Nonlinear Dynam. May 2017; 12(3): 031006. https://doi.org/10.1115/1.4035194
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