279 citations · 733 across the 42 of their papers we have counts for
49 papers
Asymptotic stability of the sine-Gordon kinks under perturbations in weighted Sobolev norms
Herbert Koch, Dongxiao Yu
We study the asymptotic stability of the sine-Gordon kinks under small perturbations in weighted Sobolev norms. Our main tool is the Bäcklund transform which reduces the study of t…
Higher Regularity of the Free Boundary in a Semilinear System
Morteza Fotouhi, Herbert Koch
In this paper we are concerned with higher regularity properties of the elliptic system \[ Δ\mathbf{u}= |\mathbf{u}|^{q-1}\mathbf{u}χ_{\{|\mathbf{u}|>0\}},\qquad\mathbf{u}=(u^1,\do…
Conserved energies for the one dimensional Gross-Pitaevskii equation: low regularity case
Herbert Koch, Xian Liao
We construct a family of conserved energies for the one dimensional Gross-Pitaevskii equation, but in the low regularity case (in \cite{KL} we have constructed conserved energies i…
Dirichlet problem for weakly harmonic maps with rough data
Gael Diebou Yomgne, Herbert Koch
Weakly harmonic maps from a domain (the upper half-space $\Rd$ or a bounded domain, ) into a smooth closed manifold are studied. Prescribing small Dirichl…
On instability mechanisms for inverse problems
Herbert Koch, Angkana Rüland, Mikko Salo
In this article we present three robust instability mechanisms for linear and nonlinear inverse problems. All of these are based on strong compression properties (in the sense of s…
Multisolitons for the cubic NLS in 1-d and their stability
Herbert Koch, Daniel Tataru
For both the cubic Nonlinear Schrödinger Equation (NLS) as well as the modified Korteweg-de Vries (mKdV) equation in one space dimension we consider the set of pure …