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The bifurcation and peakon for \(K(2, 2)\) equation with osmosis dispersion. (English) Zbl 1197.35253

Summary: The qualitative analysis methods of a dynamical system are used to investigate the peaked wave solutions of \(K(2, 2)\) equation with osmosis dispersion. The phase portrait bifurcation of the traveling wave system corresponding to the equation is given. The explicit expressions of the peaked solitary wave solution and the periodic cusp wave solution are obtained by using the portraits. The graph of the solution is given with the numerical simulation.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems
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