Modulation theory for multidimensional gravity soliton interactions in the ocean

Gravity solitons are high energy waves that are ubiquitous in shallow water, plasmas, and internal waves. Although transversely extended line solitons can be studied as exact solutions to the Kadomtsev-Petviashvili (KP) equation, a two-dimensional generalization of the Korteweg-de Vries equation, no general analytical methods for the evolution of their interactions and modulations have been found. This talk will utilize KP soliton modulation theory to model various interactions, such as a soliton emerging from a channel and a soliton incident upon an oblique corner. By interpreting these scenarios as Riemann problems in the modulation variables, we obtain analytical descriptions for line soliton dynamics that are both tractable and numerically verified. Some noteworthy results include a new interpretation of Mach reflection and the discovery of a related phenomenon called Mach expansion.