Results 71 to 80 of about 1,746 (107)

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

Integrable discretisations and Yang–Baxter maps for super nonlinear Schrödinger systems

Nuclear Physics B
We construct an integrable Grassmann-extended vertex-bond discrete system, which can be restricted to the Grassmann-extended Adler–Yamilov system of partial difference equations, and we derive a Darboux matrix and a Bäcklund transformation for the latter.
Sotiris Konstantinou-Rizos
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

A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations. [PDF]

Stoch Partial Differ Equ, 2018
Oh T, Thomann L.
europepmc   +1 more source

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation. [PDF]

Probab Theory Relat Fields, 2017
Oh T, Tzvetkov N.
europepmc   +1 more source

Local well-posedness of the periodic nonlinear Schrödinger equation with a quadratic nonlinearity ū2 in negative Sobolev spaces

, 2023
Liu R.
europepmc   +1 more source