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Soliton solutions to evolutionary PDEs arise as a balance between nonlinear and dispersive effects. However, if the dispersive term itself is nonlinear, traveling wave solutions are non-analytic. An important example of this kind of solutions are compactons: traveling waves with a compact support that interact quasi elastically. I will consider an equation in 1+1 dimensions which was proved integrable by Fokas et al. In this model, rather than interacting elastically, compacton solutions seem unstable. I will present a numerical study and try to provide an explanation.
