Boussinesq-type equations and "switching" solitons

Abstract:
It is well known that the Boussinesq equation is the bidirectional equivalent of the celebrated KdV equation. Yet, for a given unidirectional nonlinear evolution equation (NEE), it is not always apparent what should be its "Boussinesq" counterpart. Here we consider candidate Boussinesq versions of two classical unidirectional integrable equations. One of these bidirectional NEEs has soliton solutions with the unusual property that they "switch" their profiles on switching direction.