We show how the change from Eulerian to Lagrangian coordinates for the two-component Camassa–Holm system can be understood in terms of certain reparametrizations of the underlying isospectral problem. The respective ...

We analyze stability of conservative solutions of the Cauchy problem on the line for the (integrated) Hunter–Saxton (HS) equation. Generically, the solutions of the HS equation develop singularities with steep gradients ...

We introduce a novel solution concept, denotedα-dissipative solutions, that provides a continuousinterpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system ...

We establish the concept of α-dissipative solutions for the two-component Hunter–Saxton system under the assumption that either α(x)=1 or 0≤α(x)<1 for all x∈R. Furthermore, we investigate the Lipschitz stability of solutions ...

We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving ...

In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L 1 (R). In addition an Oleinik type estimate is established and some criteria on local ...

In 1991 Hunter and Saxton introduced a novel equation related to the dynamics of liquid crystals. The equation exhibited startling properties, among them wave breaking in finite time. Here we study the effects of ...

We present two initial profiles to the Camassa–Holm equation which yield solutions with accumulating breaking times

We compute explicitly the peakon-antipeakon solution of the Camassa– Holm equation ut − utxx + 3uux − 2uxuxx − uuxxx = 0 in the non-symmetric and α-dissipative case. The solution experiences wave breaking in finite time, ...