Existence and stability of standing waves for nonlinear fractional Schrödinger equation with logarithmic nonlinearity
arXiv:1701.01363 · doi:10.1016/j.na.2017.01.006
Abstract
In this paper we consider the nonlinear fractional logarithmic Schrödinger equation. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we prove that the set of minimizers is a stable set for the initial value problem, that is, a solution whose initial data is near the set will remain near it for all time.
14 pages. Some minor typos have been corrected, to appear in Nonlinear Analysis T.M.A. arXiv admin note: text overlap with arXiv:1607.01479, arXiv:1611.03319, arXiv:1608.06929
References in corpus (3)
- Orbital stability of Gausson solutions to logarithmic Schrödinger equations
- Sufficient and Necessary Conditions for the fractional Gagliardo-Nirenberg Inequalities and applications to Navier-Stokes and generalized boson equations
- Existence and stability of standing waves for nonlinear Schrodinger systems involving the fractional Laplacian
Cited by in corpus (5)
- On the dynamical nature of nonlinear coupling of logarithmic quantum wave equation, Everett-Hirschman entropy and temperature
- A note on the nonlinear Schrödinger equation in a general domain
- On instability of standing waves for the mass-supercritical fractional nonlinear Schrödinger equation
- Logarithmic Schrödinger Equations in Infinite Dimensions
- Positive multi-peak solutions for a logarithmic Schrodinger equation