The Periodic μ-b-Equation and Euler Equations on the Circle
- https://doi.org/10.1142/S1402925111001155How to use a DOI?
- μ-b-equation, diffeomorphism group of the circle, metric and non-metric Euler equations
In this paper, we study the μ-variant of the periodic b-equation and show that this equation can be realized as a metric Euler equation on the Lie group
Diff∞(𝕊) if and only if b = 2 (for which it becomes the μ-Camassa–Holm equation). In this case, the inertia operator generating the metric on Diff∞(𝕊) is given by L = μ − ∂x2. In contrast, the μ-Degasperis–Procesi equation (obtained for b = 3) is not a metric Euler equation on Diff∞(𝕊) for any regular inertia operator A ∈ ℒissym. The paper generalizes some recent results of [13, 16, 24].
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Martin Kohlmann PY - 2021 DA - 2021/01 TI - The Periodic μ-b-Equation and Euler Equations on the Circle JO - Journal of Nonlinear Mathematical Physics SP - 1 EP - 8 VL - 18 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001155 DO - https://doi.org/10.1142/S1402925111001155 ID - Kohlmann2021 ER -