6 papers
The nonlinear Quadratic Interactions of the Schrödinger type on the half-line
Isnaldo Isaac Barbosa, Márcio Cavalcante
In this work we study the initial boundary value problem associated with the coupled Schrödinger equations {with quadratic nonlinearities, that appears in nonlinear optics}, on the…
The cubic nonlinear fractional Schrödinger equation on the half-line
Márcio Cavalcante, Gerardo Huaroto
We study the cubic nonlinear fractional Schrödinger equation with Lévy indices posed on the half-line. More precisely, we define the notion of a solution for thi…
Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane
Roberto A. Capistrano-Filho, Márcio Cavalcante, Fernando A. Gallego
This paper deals with the initial-boundary value problem of the biharmonic cubic nonlinear Schrödinger equation in a quarter plane with inhomogeneous Dirichlet-Neumann boundary dat…
Well-posedness and long time behavior for the Schrödinger-Korteweg-de Vries interactions on the half-Line
Márcio Cavalcante, Adán Corcho
The initial-boundary value problem for the Schrödinger-Korteweg-de Vries system is considered on the left and right half-line for a wide class of initial-boundary data, including t…
Local well-posedness of the fifth-order KdV-type equations on the half-line
Márcio Cavalcante, Chulkwang Kwak
This paper is a continuation of authors' previous work \cite{CK2018-1}. We extend the argument \cite{CK2018-1} to fifth-order KdV-type equations with different nonlinearities, in s…
The initial-boundary value problem for the Kawahara equation on the half-line
Márcio Cavalcante, Chulkwang Kwak
This paper concerns the initial-boundary value problem (IBVP) of the Kawahara equation posed on the right and left half-lines. We prove the local well-posedness in the low regulari…