Seminar talk, 2 December 2015

From Geometry of Differential Equations
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Speaker: Stanislav Minkov

Title: Construction of recursion operators for dispersionless integrable systems (work by Artur Sergyeyev)

The talk will discuss Artur Sergyeyev's work arXiv:1501.01955 that presents a new method to construct the Lax pairs from recursion operators for a dispersionless equation and make an empiric observation that linear (in the spectral parameter) Lax pairs can give a recursion operator. Examples of Pavlov equation, heavenly equation and Alonso-Shabat equation will be discussed, with known Lax pair being made linear in the parameter by a change of variables. A few words will be told about the Hamiltonian structure of the heavenly equation.