Gérard, Patrick and Lenzmann, Enno.
(2018)
* A Lax Pair Structure for the Half-Wave Maps Equation.*
Letters in Mathematical Physics, 108 (7).
pp. 1635-1648.

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Official URL: http://edoc.unibas.ch/58405/

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## Abstract

We consider the half-wave maps equation

∂tS⃗ =S⃗ ∧|∇|S⃗ ,

where S⃗ =S⃗ (t,x) takes values on the two-dimensional unit sphere S2 and x∈R (real line case) or x∈T (periodic case). This an energy-critical Hamiltonian evolution equation recently introduced in Lenzmann and Schikorra (2017, arXiv:1702.05995v2), Zhou and Stone (Phys Lett A 379:2817–2825, 2015) which formally arises as an effective evolution equation in the classical and continuum limit of Haldane–Shastry quantum spin chains. We prove that the half-wave maps equation admits a Lax pair and we discuss some analytic consequences of this finding. As a variant of our arguments, we also obtain a Lax pair for the half-wave maps equation with target H2 (hyperbolic plane).

∂tS⃗ =S⃗ ∧|∇|S⃗ ,

where S⃗ =S⃗ (t,x) takes values on the two-dimensional unit sphere S2 and x∈R (real line case) or x∈T (periodic case). This an energy-critical Hamiltonian evolution equation recently introduced in Lenzmann and Schikorra (2017, arXiv:1702.05995v2), Zhou and Stone (Phys Lett A 379:2817–2825, 2015) which formally arises as an effective evolution equation in the classical and continuum limit of Haldane–Shastry quantum spin chains. We prove that the half-wave maps equation admits a Lax pair and we discuss some analytic consequences of this finding. As a variant of our arguments, we also obtain a Lax pair for the half-wave maps equation with target H2 (hyperbolic plane).

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Lenzmann) |
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UniBasel Contributors: | Lenzmann, Enno |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | Springer |

ISSN: | 0377-9017 |

e-ISSN: | 1573-0530 |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Identification Number: | |

Last Modified: | 01 Jun 2018 09:30 |

Deposited On: | 01 Jun 2018 09:30 |

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