18 citations · 29 across the 7 of their papers we have counts for
9 papers · 1 filter
Existence of Complementary and Variational Weak Solutions to Obstacle Problems for a Quasilinear Wave Equation
João Paulo Dias, Wladimir Neves, José Francisco Rodrigues
We prove the existence of weak solutions for the one obstacle problem associated with a class of quasilinear wave equations in one space dimension, extending previous results obtai…
On short wave-long wave interactions\\ in the relativistic context: Application to the Relativistic Euler Equations
João Paulo Dias, Hermano Frid
In this paper we introduce a model of relativistic short wave-long wave interaction where the short waves are described by the massless -dimensional Thirring model of nonlinea…
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…
Supercritical blowup in coupled parity-time-symmetric nonlinear Schrödinger equations
João-Paulo Dias, Mário Figueira, Vladimir V. Konotop +1
We prove finite time supercritical blowup in a parity-time-symmetric system of the two coupled nonlinear Schrödinger (NLS) equations. One of the equations contains gain and the oth…
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…
Finite-time blowup for a complex Ginzburg-Landau equation with linear driving
Thierry Cazenave, João Paulo Dias, Mário Figueira
In this paper, we consider the complex Ginzburg--Landau equation on , where , and . By convexity argume…
A nonlinear model describing a short wave long wave interaction in a viscoelastic medium
Paulo Amorim, João-Paulo Dias
In this paper we introduce a system coupling a nonlinear Schrödinger equation with a system of viscoelasticity, modeling the interaction between short and long waves, acting for in…
The linear stability of shock waves for the nonlinear Schrödinger-Inviscid Burgers system
Paulo Amorim, Joao-Paulo Dias, Mario Figueira +1
We investigate the coupling between the nonlinear Schrödinger equation and the inviscid Burgers equation, a system which models interactions between short and long waves, for insta…