Asymptotic stability of ground states of quadratic nonlinear Schrödinger equation with potential in 4D

Yıl 2014, Cilt: 35 Sayı: 1, 31 - 42, 19.03.2014

Özgür Mızrak

Öz

Abstract. In this paper a class of quadratic nonlinear Schrödinger equation in four space dimensions with an attractive potential is considered. We investigate asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. We show that all solutions with small initial data, converge to a nonlinear bound state. Therefore, the non-linear bound states are asymptotically stable.

Anahtar Kelimeler

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Kaynakça

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