139 citations · 534 across the 31 of their papers we have counts for
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Traveling Waves for the Nonlinear Variational Wave Equation
Katrin Grunert, Audun Reigstad
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classi…
A Regularized System for the Nonlinear Variational Wave Equation
Katrin Grunert, Audun Reigstad
We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonline…
A numerical study of variational discretizations of the Camassa-Holm equation
Sondre Tesdal Galtung, Katrin Grunert
We present two semidiscretizations of the Camassa-Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an…
Numerical conservative solutions of the Hunter--Saxton equation
Katrin Grunert, Anders Nordli, Susanne Solem
In the article a convergent numerical method for conservative solutions of the Hunter--Saxton equation is derived. The method is based on piecewise linear projections, followed by…