On the orbital stability of fractional Schr\"{o}dinger equations
Yonggeun Cho, Gyeongha Hwang, Hichem Hajaiej, and Tohru Ozawa
TL;DR
This paper proves the existence and orbital stability of standing wave solutions for fractional Schrödinger equations with power nonlinearities, establishing key properties like solution uniqueness.
Contribution
It introduces new results on the orbital stability of standing waves in fractional Schrödinger equations, including the proof of solution uniqueness.
Findings
Existence of ground state solutions.
Orbital stability of standing waves.
Uniqueness of weak solutions.
Abstract
We show the existence of ground state and orbital stability of standing waves of fractional Schr\"{o}dinger equations with power type nonlinearity. For this purpose we establish the uniqueness of weak solutions.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Spectral Theory in Mathematical Physics · Numerical methods in inverse problems