While at AIMS, Alain studied the Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation using step-like initial data along a parabolic front. He showed that employing an appropriate ansatz and a parabolic similarity reduction exactly reduces the study of such DSWs in two space-one-time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations.

Alain is currently a PhD student in applied mathematics at the University of Cape Town in South Africa.