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math.AP2021
Long-time asymptotics for an integrable evolution equation with a Lax pair
Christophe Charlier, Jonatan Lenells
We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with a Lax pair. We use the derived representation to obtain…
math.AP2018
Airy and Painlevé asymptotics for the mKdV equation
Christophe Charlier, Jonatan Lenells
We consider the higher order asymptotics for the mKdV equation in the Painlevé sector. We first show that the solution admits a uniform expansion to all orders in powers of $t^{-1/…