Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Alex H. Ardila"'
Autor:
Alex H. Ardila
Publikováno v:
Electronic Journal of Differential Equations, Vol 2016, Iss 335,, Pp 1-9 (2016)
In this article we prove of the orbital stability of the ground state for logarithmic Schrodinger equation in any dimension and under nonradial perturbations. This general stability result was announced by Cazenave and Lions [9, Remark II.3], but
Externí odkaz:
https://doaj.org/article/0ef9818611ff478bb329f69bebf4ec39
Autor:
Alex H. Ardila, Jason Murphy
Publikováno v:
Communications in Partial Differential Equations. :1-44
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7cfc3e75015284a9e763e60110af0c5a
https://doi.org/10.1080/03605302.2023.2212477
https://doi.org/10.1080/03605302.2023.2212477
Publikováno v:
Communications in Partial Differential Equations. 46:2134-2170
We study the asymptotic dynamics for solutions to a system of nonlinear Schr\"odinger equations with cubic interactions, arising in nonlinear optics. We provide sharp threshold criteria leading to global well-posedness and scattering of solutions, as
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::243ac718793be2e0910830a203c4299d
https://doi.org/10.1080/03605302.2021.1925916
https://doi.org/10.1080/03605302.2021.1925916
Autor:
Alex H. Ardila, Mykael Cardoso
Publikováno v:
Communications on Pure & Applied Analysis. 20:101-119
Using variational methods we study the stability and strong instability of ground states for the focusing inhomogeneous nonlinear Schrodinger equation (INLS) \begin{document}$ \begin{equation*} i\partial_{t}u+\Delta u+|x|^{-b}|u|^{p-1}u = 0. \end{equ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e5b8da8c1b91e04a4ea90ff70673c1f6
https://doi.org/10.3934/cpaa.2020259
https://doi.org/10.3934/cpaa.2020259
Autor:
Alex H. Ardila, Takahisa Inui
We establish the scattering of solutions to the focusing mass supercritical nonlinear Schr\"odinger equation with a repulsive Dirac delta potential \[ i\partial_{t}u+\partial^{2}_{x}u+\gamma\delta(x)u+|u|^{p-1}u=0, \quad (t,x)\in {\mathbb R}\times{\m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed58610cf358ad7bcbc4d4be973c328e
http://arxiv.org/abs/2108.00248
http://arxiv.org/abs/2108.00248
Autor:
Alex H. Ardila
In this paper, we study the nonlinear Schr\"odinger equation with focusing point nonlinearity in dimension one. First, we establish a scattering criterion for the equation based on Kenig-Merle's compactness-rigidity argument. Then we prove the energy
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21049ae0a36292d0b14918433ebcae06
http://arxiv.org/abs/2106.09139
http://arxiv.org/abs/2106.09139
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
We study the nonlinear Schrodinger equation with an arbitrary real potential $$V(x)\in (L^1+L^\infty )(\Gamma )$$ on a star graph $$\Gamma $$ . At the vertex an interaction occurs described by the generalized Kirchhoff condition with strength $$-\gam
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00e5b500624f35513bba513b3cb2a11b
http://arxiv.org/abs/2102.12001
http://arxiv.org/abs/2102.12001
Autor:
Rémi Carles, Alex H. Ardila
Publikováno v:
Communications in Mathematical Sciences
Communications in Mathematical Sciences, International Press, 2021, 19 (4), pp.993-1032. ⟨10.4310/CMS.2021.v19.n4.a6⟩
Communications in Mathematical Sciences, 2021, 19 (4), pp.993-1032. ⟨10.4310/CMS.2021.v19.n4.a6⟩
Communications in Mathematical Sciences, International Press, 2021, 19 (4), pp.993-1032. ⟨10.4310/CMS.2021.v19.n4.a6⟩
Communications in Mathematical Sciences, 2021, 19 (4), pp.993-1032. ⟨10.4310/CMS.2021.v19.n4.a6⟩
We are concerned with the global behavior of the solutions of the focusing mass supercritical nonlinear Schr{\"o}dinger equation under partial harmonic confinement. We establish a necessary and sufficient condition on the initial data below the groun
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ee90e8fb7ff063569ed4b149bcadfdf1
https://hal.archives-ouvertes.fr/hal-02864076/document
https://hal.archives-ouvertes.fr/hal-02864076/document
Autor:
Alex H. Ardila, Hichem Hajaiej
We consider the focusing mass supercritical nonlinear Schr\"odinger equation with rotation \begin{equation*} iu_{t}=-\frac{1}{2}\Delta u+\frac{1}{2}V(x)u-|u|^{p-1}u+L_{\Omega}u,\quad (x,t)\in \mathbb{R}^{N}\times\mathbb{R}, \end{equation*} where $N=2
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38fde307e10edf2bbc4dce4a06093171
http://arxiv.org/abs/2008.09907
http://arxiv.org/abs/2008.09907
Autor:
Van Duong Dinh, Alex H. Ardila
Publikováno v:
Zeitschrift für angewandte Mathematik und Physik. 71
We study the Cauchy problem for an inhomogeneous Gross-Pitaevskii equation. We first derive a sharp threshold for global existence and blow up of the solution. Then we construct and classify finite time blow up solutions at the minimal mass threshold
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f8c3010ffd632fda10bfc95b4368c53
https://doi.org/10.1007/s00033-020-01301-z
https://doi.org/10.1007/s00033-020-01301-z