A Class of Stable Perturbations for a Minimal Mass Soliton in Three-Dimensional Saturated Nonlinear Schrödinger Equations

In this result, we develop the techniques of [J. Krieger and W. Schlag, J. Amer. Math. Soc., 19 (2006), pp. 815–920] and [J. Bourgain and W. Wang, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 25 (1998), pp. 197–215] in order to determine a class of stable perturbations for a minimal mass soliton solution of a saturated, focusing nonlinear Schrodinger equation in $\mathbb{R}^3$. Using dispersive estimates proved in [J. L. Marzuola, Dispersive Estimates Using Scattering Theory for Matrix H amiltonian Equations, submitted], which are similar to those in [W. Schlag, Ann. of Math. (2), 169 (2009), pp. 139–227] and [J. Krieger and W. Schlag, J. Amer. Math. Soc., 19 (2006), pp. 815–920], by projecting an initial perturbation $\phi$ onto a subspace of the continuous spectrum of the operator $\mathcal{H}$ resulting from linearization about a minimal mass soliton $R_{min}$, we are able to use a contraction mapping similar to that from [J. Bourgain and W. Wang, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 25 (1998), pp. 1...