Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
Abstract
We consider the initial-value problem for the one-dimensional nonlinear Schrödinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as [math] . In particular, we establish the asymptotic stability of the family of small solitary waves.
Topics & Concepts
MathematicsStability (learning theory)NLSMathematical analysisDeltaTerm (time)Wave equationMathematical physicsSmall dataExponential stabilityPhysicsType (biology)Dirac delta functionClassical mechanicsCoupling (piping)Dispersive partial differential equationWave propagationInitial value problemPartial differential equationRadiationAdvanced Mathematical Physics ProblemsNonlinear Waves and SolitonsNonlinear Photonic Systems