Dissipation at singularities of the nonlinear Schrِdinger equation through limits of regularisations

The possibility of physically relevant singular solutions of the nonlinear Schrِdinger equation (NLSE) with sustained dissipation into the singularity is considered through numerical study of a dissipative regularisation and its small dissipation limit. A new form of such dissipative solutions is conjectured for certain parameter ranges where this behaviour was previously not expected, involving a multi-focusing mechanism. A possible mechanism is discussed involving a new family of stationary singular solutions of the NLSE.