Communications in Contemporary Mathematics· 2026Q1
On the Focusing Fractional Nonlinear Schrödinger Equation on the Waveguide Manifolds
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- Q1SCImago
- 2026year
Short summary
Researchers establish the existence and periodic dependence of ground states for the focusing fractional nonlinear Schrödinger equation (FNLS) on waveguide manifolds, and prove large data scattering for the anisotropic case in the intercritical regime.
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Key points
- Established existence and periodic dependence of ground states for focusing FNLS on waveguide manifolds.
- Considered both isotropic and anisotropic cases of the FNLS.
- Proved large data scattering for the anisotropic focusing FNLS in the intercritical regime.
- Utilized semivirial vanishing geometry framework for scattering results.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this paper, we consider the focusing fractional nonlinear Schrödinger equation (FNLS) on the waveguide manifolds [Formula: see text], both in the isotropic and anisotropic cases. Under different conditions, we establish the existence and periodic dependence of the ground states of the focusing FNLS. In the intercritical regime, we also establish the large data scattering for the anisotropic focusing FNLS by utilizing the framework of semivirial vanishing geometry.
The authors' abstract, as published at the source. Communications in Contemporary Mathematics, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics