Christian Klein

activity

20052026

most citedDynamics of solutions in the 1d bi-harmonic nonlinear Schrödinger equation

3 citations · 5 across the 9 of their papers we have counts for

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4 papers · 1 filter

math.AP2026

Ground states to bi-harmonic nonlinear Schrödinger equations with competing dispersion

Christian Klein, Svetlana Roudenko

We study ground-state solutions of the 4th order nonlinear Schrödinger equation with mixed dispersion via the elliptic profile equation $Δ^{2} Q + 2 a Δ Q + b Q - ∣ Q ∣^{α} Q = 0$ , focusing on…

math.AP2026

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 $L^{2}$ -critical Zakharov-Kuznetsov equation with the fractional nonlinearity $∣ u ∣^{4/3} u$ , equivalently $u^{7/3}$ for real-valued…

math.AP2025★ 3 cited

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, $i u_{t} - Δ^{2} u - 2 a Δ u + ∣ u ∣^{α} u = 0, x, a \in R$ , $α > 0$ , and investigate…

math.AP2023

Numerical study of the Serre-Green-Naghdi equations in 2D

S. Gavrilyuk, C. Klein

A detailed numerical study of solutions to the Serre-Green-Naghdi (SGN) equations in 2D with vanishing curl of the velocity field is presented. The transverse stability of line sol…