Results 41 to 50 of about 1,815 (116)

A note on Berestycki-Cazenave's classical instability result for nonlinear Schr\"odinger equations

, 2007
In this note we give an alternative, shorter proof of the classical result of Berestycki and Cazenave on the instability by blow-up for the standing waves of some nonlinear Schr\"odinger ...
Coz, Stefan Le
core   +2 more sources

Weighted Sobolev spaces and ground state solutions for quasilinear elliptic problems with unbounded and decaying potentials

, 2013
In this paper, we prove some continuous and compact embedding theorems for weighted Sobolev spaces, and consider both a general framework and spaces of radially symmetric functions.
Guoqing Zhang
semanticscholar   +1 more source

Global well-posedness for the Gross-Pitaevskii equation with an angular momentum rotational term

, 2008
In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an rotational angular momentum term in the space $\Real^2$.Comment: 10 ...
Avron, Bao, Bao, Borisov, Carles, Carles, Cazenave, Gross, Hall, Keel, Landau, Madison, Madison, Matthews, Pitaevskii, Pitaevskii, Zhang   +16 more
core   +1 more source

A new approach to linear and nonlinear Schrodinger equations using the natural decomposition method

, 2014
In this paper, we proposed a new computational algorithms called a new approach to linear and nonlinear Schrödinger equations using the Natural Decomposition Method (NDM).
Shehu Maitama
semanticscholar   +1 more source

Local minimizers for the NLS equation with localized nonlinearity on noncompact metric graphs

Open Mathematics
We investigate the existence of local minimizers for the nonlinear Schrödinger (NLS) equation with localized nonlinearity on noncompact metric graphs. In the absence of ground states, we prove that normalized local minimizers of the NLS equation do exist
Li Xiaoguang
doaj   +1 more source

Nehari-type ground state solutions for a Choquard equation with doubly critical exponents

Advances in Nonlinear Analysis, 2020
This paper deals with the following Choquard equation with a local nonlinear perturbation:
Chen Sitong, Tang Xianhua, Wei Jiuyang
doaj   +1 more source

Algebraic Lower Bounds on the Spatial Analyticity Radius for Higher Order Nonlinear Schrödinger Equations

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈ℝ,ux,0=u0x, where j ≥ 2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℝ and has a uniform radius of spatial analyticity σ0 in the space variable.
Tegegne Getachew, Birilew Belayneh, Betre Shiferaw, Huaiqin Wu   +3 more
wiley   +1 more source

Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions

Advances in Nonlinear Analysis, 2019
In the present paper, we consider the following singularly perturbed problem:
Tang Xianhua, Chen Sitong
doaj   +1 more source

Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening

Advances in Nonlinear Analysis
The Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the system and making ...
Biondini Gino, Prinari Barbara, Zhang Zechuan   +2 more
doaj   +1 more source

Global well-posedness of some high-order focusing semilinear evolution equations with exponential nonlinearity

Advances in Nonlinear Analysis, 2018
In even space dimensions, the initial value problems for some high-order focusing semilinear evolution equations with exponential nonlinearities are considered.
Saanouni Tarek
doaj   +1 more source