Zobrazeno 1 - 10
of 161
pro vyhledávání: '"Muńoz, Claudio"'
We consider the subcritical nonlinear Schr\"odinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximation of NLS solutions from the numerical and theoretical point of vie
Externí odkaz:
http://arxiv.org/abs/2409.17938
We consider the Principal Chiral Field model posed in 1+1 dimensions into the Lie group $\text{SL}(2,\mathbb R)$. In this work we show the nonlinear stability of small enough nonsingular solitons. The method of proof involves the use of vector field
Externí odkaz:
http://arxiv.org/abs/2408.09969
Autor:
Muñoz, Claudio
Dans cette thèse, nous étudions quelques propriétés dynamiques des solutions de type soliton de quelques équations dispersives nonlinéaires généralisées. La première partie de ce travail est consacrée à l'étude de l'existence, de l'unici
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00497710
http://tel.archives-ouvertes.fr/docs/00/49/77/10/PDF/thesisO.pdf
http://tel.archives-ouvertes.fr/docs/00/49/77/10/PDF/thesisO.pdf
Autor:
Muñoz, Claudio, Valenzuela, Nicolás
We present a comprehensive framework for deriving rigorous and efficient bounds on the approximation error of deep neural networks in PDE models characterized by branching mechanisms, such as waves, Schr\"odinger equations, and other dispersive model
Externí odkaz:
http://arxiv.org/abs/2405.13566
We consider the Kadomtsev-Petviashvili II (KP) model placed in $\mathbb R_t \times \mathbb R_{x,y}^2$, in the case of smooth data that are not necessarily in a Sobolev space. In this paper, the subclass of smooth solutions we study is of ``soliton ty
Externí odkaz:
http://arxiv.org/abs/2405.07125
Consider the generalized Korteweg-de Vries (gKdV) equations with power nonlinearities $q=2,3,4\ldots$ in dimension $N=1$, and the Zakharov-Kuznetsov (ZK) model with integer power nonlinearities $q$ in higher dimensions $N\geq 2$. Among these power-ty
Externí odkaz:
http://arxiv.org/abs/2404.09100
We consider the PDE flow associated to Riemann zeta and general Dirichlet $L$-functions. These are models characterized by nonlinearities appearing in classical number theory problems, and generalizing the classical holomorphic Riemann flow studied b
Externí odkaz:
http://arxiv.org/abs/2402.10154
Asymptotic stability of the fourth order $\phi^4$ kink for general perturbations in the energy space
Autor:
Maulén, Christopher, Muñoz, Claudio
The Fourth order $\phi^4$ model generalizes the classical $\phi^4$ model of quantum field theory, sharing the same kink solution. It is also the dispersive counterpart of the well-known parabolic Cahn-Hilliard equation. Mathematically speaking, the k
Externí odkaz:
http://arxiv.org/abs/2305.19222
Autor:
Morales, Matías, Muñoz, Claudio
We consider the long time behavior of solutions to scalar field models appearing in the theory of cosmological inflation (oscillons) and cold dark matter, in presence or absence of the cosmological constant. These models are not included in standard
Externí odkaz:
http://arxiv.org/abs/2305.01495
Autor:
Muñoz, Claudio, Trespalacios, Jessica
We consider the vacuum Einstein field equations under the Belinski-Zakharov symmetries. Depending on the chosen signature of the metric, these spacetimes contain most of the well-known special solutions in General Relativity, including well-known bla
Externí odkaz:
http://arxiv.org/abs/2305.01414