The hamiltonian structures of μ-equations related to periodic peakons

Fu Wei; Zhang Da-Jun; Wei Fu; Da Jun Zhang

doi:10.1088/0256-307X/30/8/080201

The hamiltonian structures of μ-equations related to periodic peakons

Fu Wei^*
, Zhang Da-Jun
, Wei Fu
, Da Jun Zhang

^*Corresponding author for this work

Shanghai University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The hierarchies of the μ-Camassa - Holm, two-component μ-Camassa - Holm and μ-modified Camassa - Holm equations are constructed from bi-Hamiltonian structures of the Korteweg-de Vries equation, the Ito equation and the modified Korteweg-de Vries equation. The key Hamiltonian operator that includes μ is ∂_xμ - ∂³x, and the inner product used to define the Jacobi identity of the Hamiltonian operators is defined on the unit circle S¹.

Original language	English
Article number	080201
Journal	Chinese Physics Letters
Volume	30
Issue number	8
DOIs	https://doi.org/10.1088/0256-307X/30/8/080201
State	Published - Aug 2013
Externally published	Yes

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Cite this

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title = "The hamiltonian structures of μ-equations related to periodic peakons",

abstract = "The hierarchies of the μ-Camassa - Holm, two-component μ-Camassa - Holm and μ-modified Camassa - Holm equations are constructed from bi-Hamiltonian structures of the Korteweg-de Vries equation, the Ito equation and the modified Korteweg-de Vries equation. The key Hamiltonian operator that includes μ is ∂xμ - ∂3x, and the inner product used to define the Jacobi identity of the Hamiltonian operators is defined on the unit circle S1.",

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N2 - The hierarchies of the μ-Camassa - Holm, two-component μ-Camassa - Holm and μ-modified Camassa - Holm equations are constructed from bi-Hamiltonian structures of the Korteweg-de Vries equation, the Ito equation and the modified Korteweg-de Vries equation. The key Hamiltonian operator that includes μ is ∂xμ - ∂3x, and the inner product used to define the Jacobi identity of the Hamiltonian operators is defined on the unit circle S1.

AB - The hierarchies of the μ-Camassa - Holm, two-component μ-Camassa - Holm and μ-modified Camassa - Holm equations are constructed from bi-Hamiltonian structures of the Korteweg-de Vries equation, the Ito equation and the modified Korteweg-de Vries equation. The key Hamiltonian operator that includes μ is ∂xμ - ∂3x, and the inner product used to define the Jacobi identity of the Hamiltonian operators is defined on the unit circle S1.

UR - https://www.scopus.com/pages/publications/84883356813

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DO - 10.1088/0256-307X/30/8/080201

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VL - 30

JO - Chinese Physics Letters

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The hamiltonian structures of μ-equations related to periodic peakons

Abstract

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