Year: 2025
Type: article
Abstract: In this pages, we consider the p order nonlinear half wave Schrödinger equations $$\begin{aligned} \left( i \partial _{t}+\partial _{x }^2-\left| D_{y}\right| \right) u=\pm |u|^{p-1} u \end{aligned}$$ i ∂ t + ∂ x 2 - D y u = ± | u | p - 1 u on the plane $$\mathbb {R}^2$$ R 2 with $$1 1 < p ≤ 2 . We prove the global well-posedness of this equation in $$L_x^2 H_y^s(\mathbb {R}^2) \cap H_x^1 L_y^2(\mathbb {R}^2)$$ L x 2 H y s ( R 2 ) ∩ H x 1 L y 2 ( R 2 ) ( $$\frac{1}{2}\le s \le 1$$ 1 2 ≤ s ≤ 1 ), which is the first global well-posedness result of nonlinear half wave Schrödinger equations. With the global well-posedness in the energy space for the focusing equation and the study on the solitary wave in Bahri et al. (Commun Contemp Math 23(05), 2020), we complete the proof of the stability of the set of ground states. Moreover, we consider the half wave Schrödinger equations on $$\mathbb {R}_{x}\times \mathbb {T}_{y}$$ R x × T y , which can also be called the wave guide Schrödinger equations on $$\mathbb {R}_{x}\times \mathbb {T}_{y}$$ R x × T y
Author: Xi Chen
Institution: University of Basel
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Universität Basel
OpenAlex ID: W4416226813