Hamiltonian partial differential equations and Painleve' transcendents (I)


Boris Dubrovin

09:20:00 - 10:50:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In the first part I will explain basic notions of geometry of weakly dispersive Hamiltonian partial differential equations (PDEs) including a perturbative approach to integrability. There are various types of phase transitions in solutions to such PDEs. Conjecturally the critical behaviour of a generic solution can be described by certain Painleve' transcendents. I will explain motivations for such Universality Conjecture and formulate rigorous results and open problems.

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