Integrable reductions of the KP-Whitham modulation system

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• Alexander Bivolcic (University at Buffalo)
• Thursday 18 August 2022, 11:30-12:00
• Seminar Room 2, Newton Institute.

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

Until recently, modulation theory has primarily been used for the study of l (1+1) dimensional nonlinear wave systems. In the last few years there have been several works aimed at generalizing and applying Whitham theory to systems in (2+1) dimensions. This talk will focus on the Whitham Modulation system for the Kadomtsev-Petviashvili (KP) equation (an integrable two-dimensional generalization of the KdV equation). As currently written, the KP-Whitham equations fail the Haantjes tensor test for integrability. Here, the two-dimensional reductions of the modulation equations are shown to be integrable. These reductions may provide clues for proving the integrability of the full KP-Whitham equations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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