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- Title
Lipschitz metric for the modified coupled Camassa–Holm system.
- Authors
Pan, Shihang
- Abstract
In this paper, we study the Lipschitz continuity of the conservative solutions for the modified coupled Camassa–Holm system on the real line. By introducing a new characteristic, the original Camassa–Holm system can be reformulated to an equivalent semilinear system in Lagrangian coordinates, and the solutions on the equivalence classes (established from the relabeling functions in Lagrangian coordinates) can construct a semigroup S^t$$ {\hat{S}}_t $$. There exists a bijection between the conservative solutions in original coordinates and the equivalence classes in Lagrangian coordinates such that we can construct a semigroup Tt$$ {\mathcal{T}}_t $$ of conservative solutions in Eulerian coordinates. Moreover, the Lipschitz continuity of the semigroup S^t$$ {\hat{S}}_t $$ ensures that the semigroup Tt$$ {\mathcal{T}}_t $$ with a new metric D^M$$ {\hat{\mathcal{D}}}^M $$ is Lipschitz continuous.
- Subjects
LIPSCHITZ continuity; LAGRANGIAN functions; BIJECTIONS
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 17, p17839
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9534