Gurevich
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On the Gurevich-Pitaevskii solution of KdV
Announce Type: cross Abstract: The universal solution of the Korteweg-de Vries equation (KdV) introduced by Gurevich and Pitaevskii in order to describe the onset of dispersive shock waves is known to also obey the self-similar reduction of the next member in the KdV hierarchy. We show that, if this common solution obeys some lower order partial differential equation, its differential order must be one, and we provide its local representation as a converging Laurent series depending on both...
Deep learning four decades of human migration
Abstract Human migration is a fundamental driver of global demographic change, shaping population structure, labour markets and social policy across countries1,2,3. Although long-term migration patterns are often linked to economic development4, they can shift rapidly in response to shocks such as conflict, environmental crises and political change5. Despite its importance, migration remains difficult to measure consistently: existing data are sparse, concentrated in high-income settings and...