Small-time asymptotics for the KdV equation show complex singularities emerging from double-pole singularities in the initial data, propagating at O(t^{-2/3}) speed governed by a Painlevé II problem with tritronquée solutions.
Fluid Mech.685, 413–439
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Small-time asymptotics and the emergence of complex singularities for the KdV equation
Small-time asymptotics for the KdV equation show complex singularities emerging from double-pole singularities in the initial data, propagating at O(t^{-2/3}) speed governed by a Painlevé II problem with tritronquée solutions.