Integrability properties of a generalised Fokker-Planck equation

Prof Luigi Martina (University of Salento, Lecce)

Tuesday 1st October 16:00-17:00 Maths 311B

Abstract

The talk aims at analysing a recently introduced generalised Fokker-Planck equation, paying particular attention to its integrability structure and solutions. 

We first show the symmetries and reductions associated with the equation, and, accordingly, identify two suitable rescalings. We proceed by discussing linearisation and bi-linearisation of the equation in terms of Hirota derivatives in the two distinct cases and show the existence of multi-kink solutions. Multi-kink solutions, in the low-viscosity regime, develop classical (viscous) shocks whose trajectories are described in terms of a geometric construction which resembles that of a tropical limit. Fusion/fission dynamics displayed by the multi-kink solutions are also presented by drawing parallels to shock collisions and particle scattering preserving total mass and momentum.  

 Integrability properties are furthermore discussed by employing Backlund transformations and identifying underlying Lax pairs. 

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