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Exact travelling wave solutions in a nonlinear elastic rod equation. (English) Zbl 1143.74033
Summary: We consider exact parametric representations of travelling wave solutions for an elastic rod equation. By using the method of plane dynamical systems, in different parameter regions, we give bifurcations of phase portraits of the travelling wave system. Exact explicit kink wave solutions, periodic wave solutions and some unbounded wave solutions are obtained.
MSC:
74J30Nonlinear waves (solid mechanics)
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics