Seminar talk, 30 November 2016

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Speaker: Maxim Pavlov

Title: New integrable discrete system

We present a new reduction of the Benney system describing propagation of long waves in fluid of finite depth. The previous model suggested by V.E. Zakharov determines the piecewise-constant velocity profile, while the new model determines the piecewise-linear velocity profile. V.E. Zakharov demonstrated that his model can be derived from the vector nonlinear Schrodinger equation by a dispersionless limit. We show that the new model can be derived from new integrable discrete system by a continuous limit.