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The hydrodynamics of soliton gases

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HY2W01 - Modulation theory and dispersive shock waves

Hydrodynamics is a powerful framework for large-wavelength phenomena in many-body systems. At its basis is the assumption that one can reduce the dynamics to that of long-lived, effective degrees of freedom obtained from the available conservation laws. In the context of conservative nonlinear dispersive equations, this is closely related to Whitham modulation theory. Recently, a hydrodynamic theory for many-body integrable systems, which accounts for their extensive number of conservation laws, was devised, called ``generalised hydrodynamics” (GHD). It is universal framework for both quantum and classical systems, and when applied to the soliton gases of integrable dispersive equations, it gives a new perspective on Whitham modulation. For instance, the condensate regime of soliton gases is much like the zero-entropy regime of quantum gases. I will review the basic aspects of GHD in the context of the KdV soliton gas, and propose some directions for future research.

This talk is part of the Isaac Newton Institute Seminar Series series.

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