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Ground states of an L2-subcritical focusing nonlinear Schrödinger (NLS) equation are known to be orbitally stable in the energy class $H^{1}(\mathbb R)$ thanks to its variational characterization. In this paper, we will show L2-stability of 1-solitons to a one-dimensional cubic NLS equation in the sense that for any initial data which are sufficiently close to a 1-soliton in $L^{2}(\mathbb R)$, th...

Backlund Transformation and L2-stability of NLS Solitons