Prof. Gino Biondini | Kadomtsev-Petviashvili equation: modulation theory, dispersive shocks

Speaker: Professor Gino Biondini (University at Buffalo)
Date: 30th Jul 2024 - 16:00 to 16:30
Venue: External
Title: Kadomtsev-Petviashvili equation: modulation theory, dispersive shocks and stationary soliton gas
Event: (PDWW01) Frontiers of Dispersive Hydrodynamics
Abstract: This talk will present some recent results about solutions of the Kadomtsev-Petviashviliequation displaying a variety of nonlinear interaction phenomena, including: (i) the timeevolution of soliton stems and bent solitons [1]; (ii) the interaction between soliton stemsand a mean flow [2]; (iii) the time evolution of wedge-shaped step-like initial conditionsand the formation of two-dimensional dispersive shocks [3]; (iv) the statistical propertiesof a stationary two-dimensional soliton gas [4].
[1] S. Ryskamp, M. Maiden, G. Biondini and M. A. Hoefer, Evolution of truncated and bentwave solitons: the Mach expansion problem, J. Fluid Mechanics 909, A24 (2021)DOI 10.1017/jfm.2020.952[2] S. Ryskamp, M. A. Hoefer and G. Biondini, Oblique interactions between solitons and mean flow in the Kadomtsev-Petviashvili equation, Nonlinearity 34, 3583 (2021)DOI 10.1088/1361-6544/abef74
[3] G. Biondini, A. Bivolcic and M. A. Hoefer, Mach reflection and expansion of two-dimensional dispersive shock waves, in preparation
[4] G. Biondini, T. Bonnemain, B. Doyon, G. A. El and G. Roberti, Two-dimensional station-ary soliton gas, in preparation
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