Solitonic connections in capillarity theory: A review
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Abstract
A review is presented here of research to date on the application of model parameter-dependent constitutive laws for which capillarity systems admit underlying solitonic structure with their characteristic key properties such as invariance under Bäcklund transformations and admittance of Painlevé reduction. The classical Korteweg capillarity system and its extensions are considered. Reductions to the canonical solitonic nonlinear Schrodinger and its resonant nonlinear Schrödinger equation extension containing a de Broglie-Bohm potential are exhibited in turn for certain model constitutive relations. A capillarity analogue of the classical Kármán-Tsien model law of gasdynamics is shown to have a key role in such canonical reductions. A novel geometric link between a Korteweg capillarity system and the classical Da Rios system of hydrodynamics is recorded. Invariance of capillarity systems under multi-parameter Bäcklund transformations is detailed and applied. Gausson and q-gaussion phenomena in certain capillarity systems is described with concomitant classes of exact solutions. A Lagrangian encapsulation of a Korteweg capillarity system is presented whereby reduction is made to the canonical Boussinesq equation.
Document Type: Invited review
Cited as: Rogers, C. Solitonic connections in capillarity theory: A review. Capillarity, 2024, 12(3): 80-88. https://doi.org/10.46690/capi.2024.09.03
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