Mixed norm estimates of Schrödinger waves and their applications [PDF]
arXiv, 2009 In this paper we establish mixed norm estimates of interactive Schr\"{o}dinger waves and apply them to study smoothing properties and global well-posedness of the nonlinear Schr\"{o}dinger equations with mass critical nonlinearity.
arxiv
A sequence of zero modes of Weyl-Dirac operators and an associated sequence of solvable polynomials [PDF]
arXiv, 2011 It is shown that a series of solvable polynomials is attached to the series of zero modes constructed by Adam, Muratori and Nash \cite ...
arxiv
Nonexistence of traveling waves for a nonlocal Gross-Pitaevskii equation [PDF]
arXiv, 2011 We consider a Gross-Pitaevskii equation with a nonlocal interaction potential. We provide sufficient conditions on the potential such that there exists a range of speeds in which nontrivial traveling waves do not ...
arxiv
Spectral Transition for Dirac Operators with Electrostatic δ -Shell Potentials Supported on the Straight Line. [PDF]
Integr Equ Oper Theory, 2022 Behrndt J, Holzmann M, Tušek M.
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The Schroedinger Equation with Potential in Random Motion [PDF]
arXiv, 2011 We study Schroedinger's equation with a potential moving along a Brownian motion path. We prove a RAGE-type theorem and Strichartz estimates for the solution on average.
arxiv
Dirac operator spectrum in tubes and layers with a zigzag-type boundary. [PDF]
Lett Math Phys, 2022 Exner P, Holzmann M.
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The pseudorelativistic Hartree equation with a general nonlinearity: existence, non existence and variational identities [PDF]
arXiv, 2012 We prove several existence and non existence results of solitary waves for a class of nonlinear pseudo-relativistic Hartree equations with general nonlinearities. We use variational methods and some new variational identities involving the half Laplacian.
arxiv
Soliton dynamics for the Schrodinger-Newton system [PDF]
arXiv, 2013 We investigate the soliton dynamics for the Schrodinger-Newton system by proving a suitable modulational stability estimates in the spirit of those obtained by Weinstein for local equations.
arxiv
Multiple $\mathbb{S}^{1}$-orbits for the Schrödinger-Newton system [PDF]
arXiv, 2013 We prove existence and multiplicity of symmetric solutions for the \emph{Schr\"odinger-Newton system} in three dimensional space using equivariant Morse theory.
arxiv
Asymptotically linear fractional Schrodinger equations [PDF]
arXiv, 2014 By exploiting a variational technique based upon projecting over the Pohozaev manifold, we prove existence of positive solutions for a class of nonlinear fractional Schrodinger equations having a nonhomogenous nonautonomous asymptotically linear nonlinearity.
arxiv