Existence of solutions to the Cauchy problem and stability of kink- solutions of the nonlinear Schrödinger equation (Q1204680)

The paper is devoted to the study of stability of kink-type solutions of the equations of the form \[ iu_ t+u_{xx}+f\bigl(| u|^ 2\bigr)u=0 \] \(x\in\mathbb{R}\), \(t>0\), \(u(x,0)=u_ 0(x)\). It is shown that under some conditions these kink solutions are stable in a certain sense.