Results 71 to 80 of about 1,721 (90)

On well-posedness of energy supercritical NLS on product space Rn×T4−n ${\mathbb{R}}^{n}{\times}{\mathbb{T}}^{4-n}$ (n = 0, 1, 2, 3)

Advances in Nonlinear Analysis
We establish the well-posedness theory for the quintic nonlinear Schrödinger equation (NLS) on four-dimensional tori (i.e., T4 ${\mathbb{T}}^{4}$ ), which is an energy-supercritical model. Compared to the recent breakthrough work (B. Kwak and S.
Wang Han, Li Xing, Lyu Ziyue, Zhao Zehua, Zhou Wenyu   +4 more
doaj   +1 more source

The nonlinear Schrödinger equation on the half-line with homogeneous Robin boundary conditions. [PDF]

Proc Lond Math Soc, 2023
Lee JM, Lenells J.
europepmc   +1 more source

Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Advanced Nonlinear Studies
Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation.
Chen Mingming, Geng Xianguo, Liu Huan
doaj   +1 more source

Nonlinear Scalar Field Equations with L2 Constraint: Mountain Pass and Symmetric Mountain Pass Approaches

Advanced Nonlinear Studies, 2019
We study the existence of radially symmetric solutions of the following nonlinear scalar field equations in ℝN{\mathbb{R}^{N}} (N≥2{N\geq 2}):
Hirata Jun, Tanaka Kazunaga
doaj   +1 more source

Regularity for critical fractional Choquard equation with singular potential and its applications

Advances in Nonlinear Analysis
We study the following fractional Choquard equation (−Δ)su+u∣x∣θ=(Iα*F(u))f(u),x∈RN,{\left(-\Delta )}^{s}u+\frac{u}{{| x| }^{\theta }}=({I}_{\alpha }* F\left(u))f\left(u),\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N⩾3N\geqslant 3, s∈12,1s\in \left ...
Liu Senli, Yang Jie, Su Yu
doaj   +1 more source

Global solutions to 3D quadratic nonlinear Schrödinger-type equation

Forum of Mathematics, Sigma
We consider the Cauchy problem to the 3D fractional Schrödinger equation with quadratic interaction of $u\bar u$ type. We prove the global existence of solutions and scattering properties for small initial data.
Zihua Guo, Naijia Liu, Liang Song
doaj   +1 more source

Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$

Forum of Mathematics, Pi
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ .
Benjamin Harrop-Griffiths, Rowan Killip, Monica Vişan   +2 more
doaj   +1 more source

Strong instability of standing waves for the Hartree equation with a constant magnetic field

Advances in Nonlinear Analysis
In this paper, we study the strong instability of standing waves for the Hartree equation with a constant magnetic field. First, we prove the existence of least action ground states for the associated stationary equation using variational methods. Second,
Mao Weifeng, Zhang Jian
doaj   +1 more source

A remark on Gibbs measures with log-correlated Gaussian fields

Forum of Mathematics, Sigma
We study Gibbs measures with log-correlated base Gaussian fields on the d-dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson’s argument.
Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo   +2 more
doaj   +1 more source

UC and BUC plane partitions

European Physical Journal C: Particles and Fields
This paper is concerned with the investigation of UC and BUC plane partitions based upon the fermion calculus approach. We construct generalized the vertex operators in terms of free charged fermions and neutral fermions and present the interlacing ...
Shengyu Zhang, Zhaowen Yan
doaj   +1 more source