Instability in nonlinear Schrödinger breathers
Instability in nonlinear Schrödinger breathers
We consider the focusing Nonlinear Schrödinger equation posed on the one dimensional line, with nonzero background condition at spatial infinity, given by a homogeneous plane wave. For this problem of physical interest, we study the initial value problem for perturbations of the background wave in Sobolev spaces. It is well-known …