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The bifurcation and peakon for Degasperis-Procesi equation. (English) Zbl 1142.35589

Summary: The analysis qualitative methods of planar dynamical systems are used to study the peaked solitary wave solutions for Degasperis-Procesi equation with the dispersion term. By using the phase portrait bifurcation of traveling wave system, periodic wave solutions and solitary wave solutions are constructed in two different ways, and their convergence is showed when \(g\) varies. The general explicit expression of peaked solitary wave solutions is obtained under some parameter conditions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35Q51 Soliton equations
37C10 Dynamics induced by flows and semiflows
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