7 papers
Review of well-posedness methods for the 1D nonlinear Schrödinger equation with an application to combined nonlinearities
Alex D. Rodriguez, Gia Azcoitia, Hannah Wubben +1
We consider the nonlinear Schrödinger equation in one dimension with nonlinearities of type for any power and review two different methods for obtaining solutions, n…
The nonlinear Schrödinger equation with combined nonlinearities in 1D
Oscar Riaño, Oscar Riaño, Alex D Rodriguez +1
We consider the one-dimensional nonlinear Schrödinger equation with the nonlinearity term that is expressed as a s…
Well-posedness of the focusing stochastic nonlinear Schrödinger equation: -critical and supercritical cases
Annie Millet, Svetlana Roudenko
We study the focusing -critical and supercritical stochastic nonlinear Schrödinger equation subject to additive or multiplicative noise. We investigate global or long time be…
Blow-up in finite or infinite time of the 2D cubic Zakharov-Kuznetsov equation
Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko +1
We prove that near-threshold negative energy solutions to the 2D cubic (-critical) focusing Zakharov-Kuznetsov (ZK) equation blow-up in finite or infinite time. The proof cons…
Nonlinear Schrödinger equation on a unit ball in one and two dimensions
Christian Klein, Svetlana Roudenko, Nikola Stoilov
We consider the nonlinear Schrödinger equation on a unit ball in one and two dimensions with Dirichlet boundary conditions, which have stabilizing effect on solutions behavior. In…
Dichotomy Results for the Electromagnetic Schrödinger Equation
Magdalena Czubak, Ian Miller, Svetlana Roudenko
The electromagnetic nonlinear Schrödinger (emNLS) equation is a variant of the well-studied nonlinear Schrödinger equation. In this article, we consider questions of global exist…