(Ce séminaire a lieu dans le cadre du séminaire tournant Bilbao-Bordeaux-Toulouse et sera retransmis depuis Toulouse). We introduce a nonlinear Schroedinger equation on the line, with a mass critical non-local cubic nonlinearity of DNLS type, which conserves the Hardy property of a Fourier transform supported in the positive half line. We identity a Lax pair for this equation, and we use this structure for studying multisoliton solutions. This a jointwork with Enno Lenzmann (Basel).