65 citations · 188 across the 24 of their papers we have counts for
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The curvature of semidirect product groups associated with two-component Hunter-Saxton systems
Martin Kohlmann
In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its -variant. Considering both equations as a geodesic flow on the semidirect product o…
Global existence and blow-up for a weakly dissipative DP equation
Martin Kohlmann
In this paper, we study a weakly dissipative variant of the periodic Degasperis-Procesi equation. We show the local well-posedness of the associated Cauchy problem in , $s>…
The periodic --equation and Euler equations on the circle
Martin Kohlmann
In this paper, we study the -variant of the periodic -equation and show that this equation can be realized as a metric Euler equation on the Lie group $\Diff^{\infty}(§)$ if…
Spectral Properties of Grain Boundaries at Small Angles of Rotation
Rainer Hempel, Martin Kohlmann
We study some spectral properties of a simple two-dimensional model for small angle defects in crystals and alloys. Starting from a periodic potential , we le…
A variational approach to dislocation problems for periodic Schrödinger operators
Rainer Hempel, Martin Kohlmann
As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential on with p…
The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
Joachim Escher, Martin Kohlmann, Jonatan Lenells
We use geometric methods to study two natural two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that these generalizations can be…
Geometric aspects of the periodic -Degasperis-Procesi equation
Joachim Escher, Martin Kohlmann, Boris Kolev
We consider the periodic $\muDP$ equation (a modified version of the Degasperis-Procesi equation) as the geodesic flow of a right-invariant affine connection on the Fréche…