Results 41 to 50 of about 1,722 (89)
Advances in Nonlinear AnalysisThe 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 +2 more
doaj +1 more source
Local minimizers for the NLS equation with localized nonlinearity on noncompact metric graphs
Open MathematicsWe 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
On extremisers to a bilinear Strichartz inequality [PDF]
, 2015 In this note, we show that a pair of Gaussian functions are extremisers to a bilinear Strichartz inequality, and unique up to the symmetry group of the inequality.Comment: 6 pages. The constant in defining the inverse Fourier transform is corrected;the
Shao, Shuanglin
core
, 2011 In a recent paper we proposed and compared various approaches to compute the ground state and dynamics of the Schr\"{o}dinger--Poisson--Slater (SPS) system for general external potential and initial condition, concluding that the methods based on sine ...
Dong, Xuanchun
core +1 more source
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
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 +16 more
core +1 more source
Existence of a Positive Solution to a Nonlinear Scalar Field Equation with Zero Mass at Infinity
Advanced Nonlinear Studies, 2018 We establish the existence of a positive solution to the ...
Clapp Mónica, Maia Liliane A.
doaj +1 more source
Ground state solutions for magnetic Schrödinger equations with polynomial growth
Advances in Nonlinear AnalysisIn this article, we investigate the following nonlinear magnetic Schrödinger equations: (−i∇+A(x))2u+V(x)u=f1(x,∣v∣2)v,(−i∇+A(x))2v+V(x)v=f2(x,∣u∣2)u,\left\{\begin{array}{l}{\left(-i\nabla +A\left(x))}^{2}u+V\left(x)u={f}_{1}\left(x,{| v| }^{2})v ...
Wu Yan, Chen Peng
doaj +1 more source
LONG TIME BEHAVIOR OF THE SOLUTIONS OF NLW ON THE $d$-DIMENSIONAL TORUS
Forum of Mathematics, Sigma, 2020 We consider the nonlinear wave equation (NLW) on the $d$-dimensional torus $\mathbb{T}^{d}$ with a smooth nonlinearity of order at least 2 at the origin. We prove that, for almost any mass, small and smooth solutions of high Sobolev indices are stable up
JOACKIM BERNIER +2 more
doaj +1 more source
Low regularity conservation laws for Fokas-Lenells equation and Camassa-Holm equation
Advances in Nonlinear AnalysisIn this article, we mainly prove low regularity conservation laws for the Fokas-Lenells equation in Besov spaces with small initial data both on the line and on the circle. We develop a new technique in Fourier analysis and complex analysis to obtain the
Shan Minjie +3 more
doaj +1 more source