Solitonic dispersive hydrodynamics and modulation theory

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• Gennady El (Northumbria)
• Thursday 06 December 2018, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. In my talk, I will present a general soliton-mean field theory to describe the propagation of solitons in macroscopic hydrodynamic flows. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham partial differential equations associated with the original dispersive hydrodynamics. Two adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. If the governing equation is integrable the soliton trapping has non-trivial implications from the viewpoint of inverse scattering theory.

Along with theoretical developments I will also present results of experiments on viscous fluid conduits that quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.

This is joint work with Mark Hoefer  (University of Colorado, Boulder).

This talk is part of the Theoretical Physics Seminars series.

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• Bham Talks
• Theoretical Physics Seminars
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