Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation
نویسندگان
چکیده
In this paper, we employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation ut−uxxt+4uux+γ(u−uxx)x = 3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the relationship among the smooth soliton solutions, the peaked solitons solution and the periodic cuspon solutions. The physical relevance of the found solutions and the reason why these solutions can exist in this equation are also given.
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