Results 41 to 50 of about 868 (80)
On multiplicity of solutions to nonlinear Dirac equation with local super-quadratic growth
Advances in Nonlinear AnalysisIn this article, we study the following nonlinear Dirac equation: −iα⋅∇u+aβu+V(x)u=g(x,∣u∣)u,x∈R3.-i\alpha \hspace{0.33em}\cdot \hspace{0.33em}\nabla u+a\beta u+V\left(x)u=g\left(x,| u| )u,\hspace{1em}x\in {{\mathbb{R}}}^{3}.
Liao Fangfang, Chen Tiantian
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Centre-of-mass motion in multi-particle Schrödinger–Newton dynamics
New Journal of Physics, 2014 We investigate the implication of the nonlinear and non-local multi-particle Schrödinger–Newton equation for the motion of the mass centre of an extended multi-particle object, giving self-contained and comprehensible derivations.
Domenico Giulini, André Großardt
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Global Analytic Solutions for the Nonlinear Schr\"odinger Equation
, 2019 We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.Comment: Corrected errors in proofs in section
Biyar, Magzhan +1 more
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Derivation of the Gross-Pitaevskii dynamics through renormalized excitation number operators
Forum of Mathematics, SigmaWe revisit the time evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. We show that the system continues to exhibit BEC once the trap has been released and that the dynamics of the condensate is described by the time-
Christian Brennecke, Wilhelm Kroschinsky
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Klein–Gordon–Maxwell Systems with Nonconstant Coupling Coefficient
Advanced Nonlinear Studies, 2018 We study a Klein–Gordon–Maxwell system in a bounded spatial domain under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static solutions.
Lazzo Monica, Pisani Lorenzo
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Nonlocal perturbations of the fractional Choquard equation
Advances in Nonlinear Analysis, 2017 We study the ...
Singh Gurpreet
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The mean-field limit for the dynamics of large particle systems
, 2003 This short course explains how the usual mean-field evolution PDEs in Statistical Physics — such as the Vlasov-Poisson, Schrodinger-Poisson or time-dependent Hartree-Fock equations — are rigorously derived from first principles, i.e. from the fundamental
F. Golse
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Global Weak Solutions of the Relativistic Vlasov-Klein-Gordon System
, 2002 We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak ...
Kunzinger, Michael +3 more
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, 2011 This article is concerned with the linearisation around a dark soliton solution of the nonlinear Schr\"odinger equation. Crucially, we present analytic expressions for the four linearly-independent zero eigenvalue solutions (also known as Goldstone modes)
Agrawal G P +12 more
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On the number of nodal domains of the 2D isotropic quantum harmonic oscillator -- an extension of results of A. Stern -- [PDF]
, 2014 In the case of the sphere and the square, Antonie Stern (1925) claimed in her PhD thesis the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contain an eigenfunction with two nodal domains. These two statements were given
Bérard, Pierre, Helffer, Bernard
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