| Abstract: |
| Until recently, Whitham modulation theory had been mostly applied to systems in one spatial dimension, but in the last few years there have been several works aimed at generalizing and applying Whitham theory to systems in two and three spatial dimensions. This talk aims to present a survey of recent results, focusing on the Kadomtsev-Petviashvili (KP) equation (the integrable two-dimensional generalization of the KdV equation) and the two-dimensional nonlinear Schrodinger (NLS) equation. I will show how Whitham modulation theory can be generalized to multidimensional nonlinear evolution equations of KP type. I will also show how the KP-Whitham system can be successfully used to characterize analytically for the first time the evolution of a variety of initial conditions, including partial soliton stems and a combination of solitons and a mean flow. Time permitting I will discuss similarities and differences between the modulation theory for the KP equation and the two-dimensional NLS equation. |
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