Results 71 to 80 of about 134 (115)

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

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

Dynamics And Bifurcations Of A Planar Map Modelling Dispersion Managed Breathers

, 1997
. We study a non-autonomous ODE with piecewise-constant coefficients and its associated two-dimensional Poincar'e mapping. The ODE models variations in amplitude and phase of a pulse propagating in a lossless optical fiber with periodically varying ...
J. Nathan Kutz, Philip Holmes
core  

The Mechanism Of The Polarizational Mode Instability In Birefringent Fiber Optics

, 2000
. We show the soliton solutions of the integrable Manakov equations exhibit an instability under arbitrarily small Hamiltonian perturbations. The instability arises from eigenvalues embedded in the essential spectrum of the associated linearized ...
Yi A. Li, Keith Promislow
core  

Inviscid Limits of the Complex Ginzburg-Landau Equation

, 2007
In the inviscid limit the generalized complex Ginzburg-Landau equation reduces to the nonlinear Schrodinger equation. This limit is proved rigorously with H 1 data in the whole space for the Cauchy problem and in the torus with periodic boundary ...
Philippe Bechouche, Ansgar Jüngel
core  

Global Existence and Uniqueness for an Optical Fiber Laser Model

, 2007
. We prove global existence and uniqueness of solutions for a modified nonlinear Schrodinger equation modeling pulse propagation in an optical fiber laser.
Er Mielkey, J. Nathan Kutz, Alexander Mielke, Philip Holmes   +3 more
core  

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

Mathematics Subject Classification. Primary 78A60, Secondary 35Q60, 35Q55. 2010 Physics and Astronomy Classification Scheme. 42.65.Re, 42.65.Sf, 42.65.Tg, 02.30.Mv

, 2010
We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions. We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope ...
Carsten Brée, Shalva Amiranashvili, Uwe Bandelow   +2 more
core  

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