Integrable systems of the intermediate long wave type in 2+1 dimensions
B. Gormley, E.V. Ferapontov, V.S. Novikov, M.V. Pavlov
TL;DR
This paper classifies 2+1 dimensional integrable systems with intermediate long wave nonlocality, linking them to waterbag systems and providing dispersive regularizations for hydrodynamic equations in shear flows.
Contribution
It introduces a classification of new integrable systems in 2+1 dimensions with nonlocality of the intermediate long wave type and explores their reductions and physical applications.
Findings
Established links to waterbag systems
Provided dispersive regularizations of hydrodynamic equations
Classified new integrable systems in 2+1 dimensions
Abstract
We classify 2+1 dimensional integrable systems with nonlocality of the intermediate long wave type. Links to the 2+1 dimensional waterbag system are established. Dimensional reductions of integrable systems constructed in this paper provide dispersive regularisations of hydrodynamic equations governing propagation of long nonlinear waves in a shear flow with piecewise linear velocity profile (for special values of vorticities).
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