Generalized Hunter–Saxton equation and the geometry of the group of circle diffeomorphisms

By B. Khesin, Jonatan Lenells, G. Misiołek. 2008

144 citations recorded by the source corpus.

We study an equation lying ‘mid-way’ between the periodic Hunter–Saxton and Camassa–Holm equations, and which describes evolution of rotators in liquid crystals with external magnetic field and self-interaction. We prove that it is an Euler equation on the diffeomorphism group of the circle corresponding to a natural right-invariant Sobolev metric. We show that the equation is bihamiltonian and admits both cusped and smooth traveling-wave solutions which are natural candidates for solitons. We also prove that it is locally well-posed and establish results on the lifespan of its solutions. Throughout the paper we argue that despite similarities to the KdV, CH and HS equations, the new equation manifests several distinctive features that set it apart from the other three.

View Paper: https://www.semanticscholar.org/paper/201a7d47922b0e2b61cce8df9c346417d2b79a3a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Changzheng Qu
2. Ying Fu
3. Yue Liu
4. Robin Ming Chen
5. Zhaoyang Yin

Citations in the corpus

• Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, background): “Its integrability, well-posedness, blow-up and peakons were discussed in [20,30].”