21 citations · 68 across the 22 of their papers we have counts for
23 papers
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…
Multi-domain spectral approach for Zakharov-Kuznetsov equations in 3D with cylindrical symmetry
Christian Klein, Svetlana Roudenko, Nikola Stoilov
We present a novel numerical framework for studying nonlinear dispersive equations in higher-dimensional settings, specifically designed for solutions featuring traveling waves alo…
Nonlinear Schrödinger equation on a unit ball in one and two dimensions
Christian Klein, Svetlana Roudenko, Nikola Stoilov
We investigate the nonlinear Schrödinger equation on a unit ball in one and two dimensions with Dirichlet boundary condition, focusing on ground states, their limiting behavior, st…
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…
Multi-domain spectral approach to rational-order fractional derivatives
C. Klein, N. Stoilov
We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is…
Numerical study of the transverse stability of line solitons of the Zakharov-Kuznetsov equations
Christian Klein, Jean-Claude Saut, Nikola Stoilov
We present a detailed numerical study of the stability under periodic perturbations of line solitons of two-dimensional, generalized Zakharov-Kuznetsov equations with various power…
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…
Spectral approach to Korteweg-de Vries equations on the compactified real line
C. Klein, N. Stoilov
We present a numerical approach for generalised Korteweg-de Vries (KdV) equations on the real line. In the spatial dimension we compactify the real line and apply a Chebyshev collo…
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…
Multi-domain spectral approach for the Hilbert transform on the real line
C. Klein, J. Riton, N. Stoilov
A multi-domain spectral method is presented to compute the Hilbert transform on the whole compactified real line, with a special focus on piece-wise analytic functions and function…
Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation
C. Klein, S. Roudenko, N. Stoilov
We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Kortewe…
Large behavior of d-bar problems for domains with a smooth boundary
C. Klein, Johannes Sjöstrand, N. Stoilov
In a previous work on the large behavior of complex geometric optics solutions to a system of d-bar equations, we treated in detail the situation when a certain potential is…
Large behavior of complex geometric optics solutions to d-bar problems
C. Klein, J. Sjöstrand, N. Stoilov
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 integrable Davey-Stew…
Numerical study of Zakharov-Kuznetsov equations in two dimensions
C. Klein, S. Roudenko, N. Stoilov
We present a detailed numerical study of solutions to the (generalized) Zakharov-Kuznetsov equation in two spatial dimensions with various power nonlinearities. In the -subc…
High precision numerical approach for the Davey-Stewartson II equation for Schwartz class initial data
C. Klein, K. McLaughlin, N. Stoilov
We present an efficient high-precision numerical approach for the Davey-Stewartson (DS) II equation, treating initial data from the Schwartz class of smooth, rapidly decreasing fun…
Numerical study of the transverse stability of the Peregrine solution
C. Klein, N. Stoilov
We generalise a previously published approach based on a multi-domain spectral method on the whole real line in two ways: firstly, a fully explicit 4th order method for the time in…
Multidomain spectral method for the Gauss hypergeometric function
S. Crespo, M. Fasondini, C. Klein +2
We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius' m…
Spectral approach to the scattering map for the semi-classical defocusing Davey-Stewartson II equation
C. Klein, K. McLaughlin, N. Stoilov
The inverse scattering approach for the defocusing Davey-Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar pro…
Numerical scattering for the defocusing Davey-Stewartson II equation for initial data with compact support
C. Klein, N. Stoilov
In this work we present spectral algorithms for the numerical scattering for the defocusing Davey-Stewartson (DS) II equation with initial data having compact support on a disk, i.…
Numerical Approach to Painlevé Transcendents on Unbounded Domains
Christian Klein, Nikola Stoilov
A multidomain spectral approach for Painlevé transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a, possibly divergen…
Numerical study of blow-up mechanisms for Davey-Stewartson II systems
C. Klein, N. Stoilov
We present a detailed numerical study of various blow-up issues in the context of the focusing Davey-Stewartson II equation. To this end we study Gaussian initial data and perturba…
'Riemann Equations' in Bidifferential Calculus
Oleksandr Chvartatskyi, Folkert Mueller-Hoissen, Nikola Stoilov
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential…