On a Boussinesq Capillarity System: Hamiltonian Reductions and Associated Quartic Geometries

Abstract

A nonlinear Boussinesq-type capillarity model system is shown to admit exact reductions to coupled Hamiltonian subsystems associated with time-modulated quartic density distributions. In particular, in 3+1 dimensions, time-modulated "red blood cell" geometries for the density distribution are isolated.

The Korteweg capillarity system. Integrable reduction via gauge and reciprocal links

“…This novel reduction and one associated with the classical Boussinesq capillarity system were linked to the motion of curves in Euclidean and projective space and solitonic connections again established. It is noted that quartic surface geometries admitted by a nonlinear Boussinesq capillarity system have recently been investigated in [49] and, in particular, time-modulated 'red blood cell' geometry for the density distribution isolated.…”