Mathematics Graduate Students Organization

Seminar:

Date: November 8

Non-linear hyperbolic equations without dispersive and/or dissipative terms may develop shocks. With the appropriate presence of dispersion, the shock may be avoided breaking up the propagating wave into solitary waves, each traveling at different speed. An example of this phenomenon is present in the KdV equation, which develops solitary waves known as solitons. In heterogeneous periodic media, dispersion may occur due to effective reflections between the material interfaces making non-linear waves to break up into solitary waves. During this presentation, this phenomenon will be better explained mainly based on numerical simulations.
Simulations in 1D will be first considered using the non-linear p-system on heterogeneous periodic media where solitary waves, known as stegotons, are developed. Finally, the same phenomenon will be presented in two dimensions on different settings using the non-linear 2D p-system, something, as far as we know, never studied before. Here, I will present two completely different kinds of 2D solitary waves being formed due to dispersion introduced by heterogeneity of the media.