Abstract
A Lagrangian version of the classical 1+1-dimensional Korteweg capillarity system is shown to encapsulate as a particular reduction an integrable Boussinesq equation. The associated integrability of the corresponding Eulerian capillarity system is set down. In turn, hidden integrability cases of the generalised Boussinesq equation are recorded associated with reduction of the Eulerian system to the integrable cubic and resonant nonlinear Schrodinger equations together with extensions obtained by application of invariance under a reciprocal transformation.
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