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On the Lagrangian version of the Korteweg capillarity system: integrability aspects

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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 Schrödinger equations together with extensions obtained by application of invariance under a reciprocal transformation.

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  1. School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia

    Colin Rogers

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Rogers, C. On the Lagrangian version of the Korteweg capillarity system: integrability aspects. Ricerche mat 71, 29–39 (2022). https://doi.org/10.1007/s11587-020-00531-7

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