Justification of Peregrine soliton from full water waves

Qingtang Su

The Peregrine soliton $Q(x,t)=e^{it}(1-\frac{4(1+2it)}{1+4x^2+4t^2})$ is an exact solution of the 1d focusing nonlinear schrödinger equation (NLS) $i{B}_t+B_{xx}=-2|B{|}^{2}B$, having th…