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The KdV equation: exponential asymptotics, complex singularities and Painlevé II
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We apply techniques of exponential asymptotics to the KdV equation to derive the small-time behaviour for dispersive waves that propagate in one direction. The results demonstrate how the amplitude, wavelength and speed of these waves depend on the strength and location of complex-plane singularities of the initial condition. Using matched asymptotic expansions, we show how the small-time dynamics of complex singularities of the time-dependent solution are dictated by a Painlevé II problem with decreasing tritronquée solutions. We relate these dynamics to the solution on the real line.
Date:
6 November 2025, 12:00
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Venue Details:
L3
Speaker:
Prof. Scott W McCue (Queensland University of Technology Brisbane)
Organiser:
Alain Goriely (University of Oxford)
Organiser contact email address:
abcnichola@gmail.com
Part of:
Industrial & Applied Mathematics Seminar
Booking required?:
Not required
Cost:
Free
Audience:
Members of the University only
Editor:
Nicola Kirkham
