Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Orbital stability and uniqueness of the ground state for the non-linear Schrödinger equation in dimension one

Pages: 4309 - 4328, Volume 37, Issue 8, August 2017      doi:10.3934/dcds.2017184

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Daniele Garrisi - West Building, Oce No. 5W443, Department of Mathematics Education, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon, 402-751, South Korea (email)
Vladimir Georgiev - Dipartimento di Matematica, Largo Bruno Pontecorvo n. 5, 56127, Pisa (PI), Italy (email)

Abstract: We prove that standing-waves which are solutions to the non-linear Schrödinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.

Keywords:  Stability, uniqueness, Schrödinger.
Mathematics Subject Classification:  Primary: 35Q55; Secondary: 47J35.

Received: November 2016;      Revised: March 2017;      Available Online: April 2017.