Matthew Tranter: "Resolution of zero-mass contradiction"

Boussinesq-type equations are used to describe long weakly-nonlinear longitudinal strain waves in a bi-layer. The traditional method of deriving reduced uni-directional models can impose a "zero-mass constraint”, i.e. the initial conditions should necessarily have zero mean, restricting the applicability of that description. In this talk we will discuss how solutions can be constructed on the periodic domain that bypass the contradiction, for Boussinesq-Klein-Gordon and coupled Boussinesq equations, using asymptotic multiple-scale expansions involving two pairs of fast characteristic variables and two slow-time variables. We will numerically show the asymptotic validity of the solutions and study the effect of wave interactions, from solitary wave or cnoidal wave initial conditions. We will also explore recent developments in the scattering of wave packets, using zero-mass initial conditions to circumvent the contradiction in this case. Based on joint papers with K. Khusnutdinova and J. Tamber.