Abstract: We consider the periodic fractional nonlinear Schrödinger equation where the nonlinearity term is expressed in two ways: the first one whose derivatives have a type of polynomial decay; the second one is given by a sum of powers, possibly infinite. By using standard properties of periodic Sobolev spaces, we study the local well-posedness for the Cauchy problem when initial data satisfy a non-vanishing condition.
Partial Differential Equations and Applications, volume 6, article number 23, April 2025
Preprint: https://arxiv.org/abs/2410.08144v1