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The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics

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CATW04 - Complex analysis: techniques, applications and computations - perspectives in 2023

We study a prototypical example in nonlinear dynamics where transition to self-similarity in a singular limit is fundamentally changed as a parameter is varied. We focus on the complicated dynamics that occur in a generalised unstable thin-film equation that yields finite-time rupture. A parameter, n, is introduced to model more general disjoining pressures. For the standard case of van der Waals intermolecular forces, n = 3, it was previously established that a countably infinite number of self-similar solutions exist leading to rupture. However, recent numerical results have demonstrated the surprising complexity that exists for general values of n. In particular, the bifurcation structure of self-similar solutions now exhibits branch merging as n is varied. We shall present key ideas of how branch merging can be interpreted via exponential asymptotics.

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

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Room 2, Central Lecture Block, Sidgwick Site Old Cavendish Psychology Second Floor Seminar Room SCR, 17 Mill Lane

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