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The 3D critical Zakharov--Kuznetsov equation: blow-up and soliton dynamics
Christian Klein, Svetlana Roudenko, Nikola Stoilov
We study the full three-dimensional dynamics of the -critical Zakharov-Kuznetsov equation with the fractional nonlinearity , equivalently for real-valued…
Numerical study of the 2D Kaup-Broer-Kuperschmidt Boussinesq system
Théo Gaudry, Christian Klein, Jean-Claude Saut +1
In this work we consider the well posed version of the Kaup-Broer-Kuperschmidt system in two dimensions. We numerically construct soliton type solutions and show that they are unst…
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…
Dynamics of solutions in the 1d bi-harmonic nonlinear Schrödinger equation
Christian Klein, Iryna Petrenko, Svetlana Roudenko +1
We consider the one dimensional 4th order, or bi-harmonic, nonlinear Schrödinger (NLS) equation, namely, , , and investigate…
Large behavior for the reflection coefficient for Davey-Stewartson II equations
Christian Klein, Johannes Sjöstrand, Nikola Stoilov
The study of complex geometric optics solutions to a system of d-bar equations appearing in the context of electrical impedance tomography and the scattering theory of the integrab…
Numerical study of Davey-Stewartson I systems
J. Frauendiener, C. Klein, U. Muhammad +1
An efficient high precision hybrid numerical approach for integrable Davey-Stewartson (DS) I equations for trivial boundary conditions at infinity is presented for Schwartz class i…