Abstract
We show that the physical Hastings–McLeod solution of the integrable Painlevé II equation generalizes in a natural way to a class of non-integrable equations, in a way that preserves many of the significant qualitative properties. The Hastings–McLeod solution of Painlevé II is an important and universal example of resurgent relations between perturbative and non-perturbative physics. We derive the trans-series structure of the generalized Hastings–McLeod solutions, demonstrating that integrability is not essential for the resurgent asymptotic properties of the solutions.
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