-
Previous Article
Poisson brackets in Hydrodynamics
- DCDS Home
- This Issue
-
Next Article
Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity
Conformal and Geometric Properties of the Camassa-Holm Hierarchy
1. | School of Mathematics, Trinity College Dublin, Dublin 2, Ireland |
  The squared eigenfunctions of the spectral problem, associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform (IST) for the Camassa-Holm hierarchy as a Generalised Fourier Transform (GFT). Using GFT we describe explicitly some members of the CH hierarchy, including integrable deformations for the CH equation. Also we show that solutions of some 2+1-dimensional generalizations of CH can be constructed via the IST for the CH hierarchy.
[1] |
Pengliang Xu, Xiaomin Tang. Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra. Electronic Research Archive, 2021, 29 (4) : 2771-2789. doi: 10.3934/era.2021013 |
[2] |
Navin Keswani. Homotopy invariance of relative eta-invariants and $C^*$-algebra $K$-theory. Electronic Research Announcements, 1998, 4: 18-26. |
[3] |
Hongyan Guo. Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra. Electronic Research Archive, 2021, 29 (4) : 2673-2685. doi: 10.3934/era.2021008 |
[4] |
Wenjun Liu, Yukun Xiao, Xiaoqing Yue. Classification of finite irreducible conformal modules over Lie conformal algebra $ \mathcal{W}(a, b, r) $. Electronic Research Archive, 2021, 29 (3) : 2445-2456. doi: 10.3934/era.2020123 |
[5] |
Mark Wilkinson. A Lie algebra-theoretic approach to characterisation of collision invariants of the Boltzmann equation for general convex particles. Kinetic and Related Models, 2022, 15 (2) : 283-315. doi: 10.3934/krm.2022008 |
[6] |
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa, Akito Suzuki, Kanako Suzuki. Scattering and inverse scattering for nonlinear quantum walks. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3687-3703. doi: 10.3934/dcds.2018159 |
[7] |
Francesco Demontis, Cornelis Van der Mee. Novel formulation of inverse scattering and characterization of scattering data. Conference Publications, 2011, 2011 (Special) : 343-350. doi: 10.3934/proc.2011.2011.343 |
[8] |
Leonardo Marazzi. Inverse scattering on conformally compact manifolds. Inverse Problems and Imaging, 2009, 3 (3) : 537-550. doi: 10.3934/ipi.2009.3.537 |
[9] |
Siamak RabieniaHaratbar. Inverse scattering and stability for the biharmonic operator. Inverse Problems and Imaging, 2021, 15 (2) : 271-283. doi: 10.3934/ipi.2020064 |
[10] |
Frank Hettlich. The domain derivative for semilinear elliptic inverse obstacle problems. Inverse Problems and Imaging, 2022, 16 (4) : 691-702. doi: 10.3934/ipi.2021071 |
[11] |
Fenglong Qu, Jiaqing Yang. On recovery of an inhomogeneous cavity in inverse acoustic scattering. Inverse Problems and Imaging, 2018, 12 (2) : 281-291. doi: 10.3934/ipi.2018012 |
[12] |
Peter Monk, Jiguang Sun. Inverse scattering using finite elements and gap reciprocity. Inverse Problems and Imaging, 2007, 1 (4) : 643-660. doi: 10.3934/ipi.2007.1.643 |
[13] |
Johannes Elschner, Guanghui Hu. Uniqueness in inverse transmission scattering problems for multilayered obstacles. Inverse Problems and Imaging, 2011, 5 (4) : 793-813. doi: 10.3934/ipi.2011.5.793 |
[14] |
Simopekka Vänskä. Stationary waves method for inverse scattering problems. Inverse Problems and Imaging, 2008, 2 (4) : 577-586. doi: 10.3934/ipi.2008.2.577 |
[15] |
Peijun Li, Xiaokai Yuan. Inverse obstacle scattering for elastic waves in three dimensions. Inverse Problems and Imaging, 2019, 13 (3) : 545-573. doi: 10.3934/ipi.2019026 |
[16] |
Fang Zeng. Extended sampling method for interior inverse scattering problems. Inverse Problems and Imaging, 2020, 14 (4) : 719-731. doi: 10.3934/ipi.2020033 |
[17] |
Michele Di Cristo. Stability estimates in the inverse transmission scattering problem. Inverse Problems and Imaging, 2009, 3 (4) : 551-565. doi: 10.3934/ipi.2009.3.551 |
[18] |
Gabriel Katz. Causal holography in application to the inverse scattering problems. Inverse Problems and Imaging, 2019, 13 (3) : 597-633. doi: 10.3934/ipi.2019028 |
[19] |
Fang Zeng, Pablo Suarez, Jiguang Sun. A decomposition method for an interior inverse scattering problem. Inverse Problems and Imaging, 2013, 7 (1) : 291-303. doi: 10.3934/ipi.2013.7.291 |
[20] |
Qinghua Wu, Guozheng Yan. The factorization method for a partially coated cavity in inverse scattering. Inverse Problems and Imaging, 2016, 10 (1) : 263-279. doi: 10.3934/ipi.2016.10.263 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]