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Dispersive Shock Waves in Lattices: A Dimension Reduction Approach

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HY2W01 - Modulation theory and dispersive shock waves

Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state.The primary tool for the analytical study of DSWs is Whitham’s modulation theory.While this framework has been successfully employed in many space-continuous settingsto describe DSWs, the Whitham modulation equations are virtually intractable in mostspatially discrete systems. In this talk, we explore other avenues to elucidateproperties of lattice DSWs that are based on reducing the dynamics to a low dimensional ODE . Connection of these results to Whitham modulation theory will also be discussed.

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

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