Noticias en español
Parabolic trapped subvarieties in globally hyperbolic spacetimes.
Abstract: Abstract: Since 1965 when Penrose defined the concept of a trapped surface (compact and without boundary) in a 4-dimensional space-time, these surfaces have been an important object of study for geometricians and theoretical physicists, standing out for their mathematical properties as well as for their applications in general relativity. Trapped surfaces can be defined in terms of the causal character of their mean curvature vector, which allows us to generalize them to subvarieties, not necessarily compact and of any dimension and/or codimension, in space-time. In this...
Read More“Classification of Semigraphical Translators: The yeti doesn’t exist!”
Abstract: In this talk I will discuss the non-existence of certain solutions to the equation that determines translating solutions to Mean Curvature Flow. This result completes the classification to semigraphical translators.
Read MoreMultiple normalized solutions to a system of nonlinear Schrödinger equations.
Abstract: We present recent results concerning normalized solutions to a system of coupled nonlinear Schr¨odinger equations. The problem appears in different areas of mathematical physics, e.g. in the analysis of Bose-Einstein condensation or in nonlinear optics. By means of spectral results, the Cwikel-Lieb-Rozenblum theorem, the Morse index and new Liouville-type results we show the existence of multiple normalized solutions for sufficiently large coupling. The talk is based on joint work with Andrzej Szulkin.
Read MoreError bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains.
Abstract: We consider the subcritical nonlinear Schrödinger (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 view in the case of bounded domains. In this paper, we introduce a PINNs method to treat the case of unbounded domains and show rigorous bounds on the associated approximation error in terms of the energy and Strichartz norms, provided reasonable integration schemes are available. Applications to traveling waves, breathers and solitons, as...
Read MoreNonexistence and uniqueness of breathers for modified Zakharov-Kuznetsov models.
Abstract: In this talk we will consider the (focusing) modi ed Zakharov-Kuznetsov (mZK) in dimension N ≥ 1: ut + (∆u + 2u3)x1 = 0,for a given real-valued function u = u(t, x), where t ∈ R and x ∈ RN . This equation is a specialcase of the completely integrable modi ed Korteweg-de Vries (mKdV) equation ut + (uxx +2u3)x = 0. During this talk we will present results related to existence and nonexistence of quasimonochromatic breathers solution for the mZK equation, depending on the dimnesion N . Additionally we will show how the famous breather solution of the mKdV equation...
Read MoreOn the Asymptotic Stability of Solitary Wave Solutions to the Boussinesq Model in the Energy Space.
Abstract: The Good Boussinesq (GB) model is known to admit solitary wave solutions with speeds in the range −1<c<1. In this talk, we revisit existing results and present new findings on the asymptotic stability of solitary wave solutions to the GB equation with power-type nonlinearity and general initial data in the energy space H1xL2. These new result complete the orbital stability stability result established by Bona and Sachs (1988). The proof employs a novel set of virial estimates specifically tailored to the GB system in a moving frame. In particular, we introduce a...
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