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Bifurcations and exact bounded travelling wave solutions for a partial differential equation. (English) Zbl 1181.35214
Summary: A partial differential equation is investigated by using the bifurcation theory and the method of phase portraits analysis, the existence of loop soliton, peakon, generalized compacton, smooth and non-smooth periodic waves, breaking kink and anti-kink waves is proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some conditions, exact parametric representations of these waves in explicit and implicit forms are obtained.

MSC:
35Q51 Soliton equations
35C07 Traveling wave solutions
35C08 Soliton solutions
35B10 Periodic solutions to PDEs
37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
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