# On the reduced Maxwell-Bloch equations

**Date**: Friday 3 November 2017, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Applied Mathematics seminars, Integrable systems seminars, Seminar series**Cost**: Free

#### Alexis Arnaudon, Imperial College London. Part of the integrable systems seminars series.

In this talk, I will show how the so-called reduced Maxwell-Bloch (RMB) equation is a member of a family of four integrable equations, differentiated by only a couple of signs. The original RMB equation arose as an approximation of the self-induced transparency theory describing the interaction between light and a polarized medium. I will show that one of the new equations, called the hyperbolic RMB equation, can be derived in the context of strongly correlated Bose-Einstein condensates (BECs). In this framework, the light is replaced by the condensate and the polarized medium corresponds to the excited particles around the BEC. I will also show some properties of these four equations such as modulational instability and soliton solutions.

Tea and coffee will be available at 3.40pm on level 9 of the School of Mathematics.

**Alexis Arnaudon,** *Imperial College London*