3 citations · 11 across the 13 of their papers we have counts for
17 papers
Sharp local well-posedness and nonlinear smoothing for dispersive equations through frequency-restricted estimates
Simão Correia, Filipe Oliveira, Jorge Drumond Silva
We consider the problem of establishing nonlinear smoothing as a general feature of nonlinear dispersive equations, i.e. the improved regularity of the integral term in Duhamel's f…
Quadratic Symmetric Polynomials and an analogue of the Davenport Constant
Hemar Godinho, Abílio Lemos, Victor Neumann +1
In this paper, we define the constant , an analogue for the Davenport constant, for sequences on the finite field , defined via quadratic symmetric polynomia…
On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
Vanessa Barros, Simão Correia, Filipe Oliveira
We study the nonlinear Schrödinger equation with initial data in , where and $2<p<2…
Mass-transfer instability of ground-states for Hamiltonian Schrödinger systems
Simão Correia, Filipe Oliveira, Jorge D. Silva
We study generic semilinear Schrödinger systems which may be written in Hamiltonian form. In the presence of a single gauge invariance, the components of a solution may exchange ma…
Weighted EGZ Constant for p-groups of rank 2
Filipe Oliveira, Abílio Lemos, Hemar Godinho
Let be a finite abelian group of exponent , written additively, and let be a subset of . The constant is defined as the smallest integer such…
On a Schrödinger system arizing in nonlinear optics
Filipe Oliveira, Ademir Pastor
We study the nonlinear Schrödinger system \[ \begin{cases} \displaystyle iu_t+Δu-u+(\frac{1}{9}|u|^2+2|w|^2)u+\frac{1}{3}\overline{u}^2w=0,\\ i\displaystyle σw_t+Δw-μw+(9|w|^2+2|u|…
Scattering theory for the Schrödinger-Debye System
Simão Correia, Filipe Oliveira
We study the Schrödinger-Debye system over iu_t+\frac 12Δu=uv,\quad μv_t+v=λ|u|^2 and establish the global existence and scattering of small solutions for initial da…
On a nonlinear Schrödinger system arising in quadratic media
Adán Corcho, Simão Correia, Filipe Oliveira +1
We consider the quadratic Schrödinger system where , in…
On a coupled system of a Ginzburg-Landau equation with a quasilinear conservation law
João-Paulo Dias, Filipe Oliveira, Hugo Tavares
We study the Cauchy problem for a coupled system of a complex Ginzburg-Landau equation with a quasilinear conservation law $$ \left\{\begin{array}{rlll} e^{-iθ}u_t&=&u_{xx}-|u|^2u-…
On a quasilinear non-local Benney System
João-Paulo Dias, Filipe Oliveira
We study the quasilinear non-local Benney System $$\left\{\begin{array}{llll} iu_t+u_{xx}=|u|^2u+buv\\ v_t+a(\int_{\mathbf{R}^+}v^2dx)v_x=-b(|u|^2)_x,\quad (x,t)\in\mathbf{R}^+\tim…
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with equations
Simão Correia, Filipe Oliveira, Hugo Tavares
In this work we consider the weakly coupled Schrödinger cubic system \[ \begin{cases} \displaystyle -Δu_i+λ_i u_i= μ_i u_i^{3}+ u_i\sum_{j\neq i}b_{ij} u_j^2 \\ u_i\in H^1(\mathbb{…
Ground States for a nonlinear Schrödinger system with sublinear coupling terms
Filipe Oliveira, Hugo Tavares
We study the existence of ground states for the coupled Schrödinger system \begin{equation} \left\{\begin{array}{lll} \displaystyle -Δu_i+λ_i u_i= μ_i |u_i|^{2q-2}u_i+\sum_{j\neq i…
Ground states for a coupled nonlinear Schrödinger system
Filipe Oliveira
We study the existence of ground states for the coupled Schrödinger system \begin{equation} \label{ellipticabstract} \left\{ \begin{array}{llll} -Δu+u&=&|u|^{2q-2}u+b|v|^q|u|^{q-2}…
A note on the existence of traveling-wave solutions to a Boussinesq system
Filipe Oliveira
We obtain a one-parameter family of traveling-wave solutions to the Boussinesq system $$u_t+η_x+uu_x+cη_…
Existence and linearized stability of solitary waves for a quasilinear Benney system
João-Paulo Dias, Mário Figueira, Filipe Oliveira
We prove the existence of solitary wave solutions to the quasilinear Benney system where , and $a…
Local and Global Well-Posedness for the Critical Schrodinger-Debye System
Adan J. Corcho, Filipe Oliveira, Jorge Drumond Silva
We establish local well-posedness results for the Initial Value Problem associated to the Schrödinger-Debye system in dimensions for data in , with …
On The Cauchy Problem for the elliptic Zakharov-Schulman system in dimensions 2 and 3
Filipe Oliveira, Mahendra Panthee, Jorge Drumond Silva
We prove that the Cauchy problem associated to the Zakharov-Schulman system , is locally well-posed for given initial data in Sobolev spaces $H^s(R^…