Static solitary waves as limits of discretization: A plausible argument

We investigate special limits of the classical Euler buckling problem, arguing that the solution-family 'imitating' (without mass forces) the propagation of a dynamic solitary wave cannot be obtained as a limit from Euler's problem, only from its discretized version. Although we can not prove this claim rigorously, we prove other related statements that make the conjecture strongly plausible. Our results yield access to some open questions related to the discretized problem; also they show some new aspects of spatially chaotic behaviour.