ORBITAL STABILITY FOR THE MASS-CRITICAL AND SUPERCRITICAL PSEUDO-RELATIVISTIC NONLINEAR SCHRODINGER EQUATION

초록

For the one-dimensional mass-critical and supercritical pseudo-relativistic nonlinear Schrodinger equation, a stationary solution can be con-structed as an energy minimizer under an additional kinetic energy constraint and the set of energy minimizers is orbitally stable [2]. In this study, we proved the local uniqueness and established the orbital stability of the solitary wave by improving that of the energy minimizer set. A key aspect thereof is the re-formulation of the variational problem in the non-relativistic regime, which we consider to be more natural because the proof extensively relies on the sub crit-ical nature of the limiting model. Thus, the role of the additional constraint is clarified, a more suitable Gagliardo-Nirenberg inequality is introduced, and the non-relativistic limit is proved. Subsequently, this limit is employed to derive the local uniqueness and orbital stability.

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