29 citations · 47 across the 12 of their papers we have counts for
5 papers · 1 filter
On a nonlocal hyperbolic conservation law arising from a gradient constraint problem
Paulo Amorim
In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the…
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…
Convergence of a numerical scheme for a coupled Schrödinger--KdV system
Paulo Amorim, Mário Figueira
We prove the convergence in a strong norm of a finite difference semi-discrete scheme approximating a coupled Schrödinger--KdV system on a bounded domain. This system models the in…
Convergence of a finite difference method for the KdV and modified KdV equations with data
Paulo Amorim, Mário Figueira
We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in ), wi…
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…