Zobrazeno 1 - 10
of 111
pro vyhledávání: '"Caudrelier, Vincent"'
Generalised Hydrodynamics (GHD) describes the large-scale inhomogeneous dynamics of integrable (or close to integrable) systems in one dimension of space, based on a central equation for the fluid density or quasi-particle density: the GHD equation.
Externí odkaz:
http://arxiv.org/abs/2406.04924
Publikováno v:
SIGMA 20 (2024), 100, 30 pages
We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoint orbits.
Externí odkaz:
http://arxiv.org/abs/2405.12837
Autor:
Li, Luen-Chau, Caudrelier, Vincent
The study of the set-theoretic solutions of the reflection equation, also known as reflection maps, is closely related to that of the Yang-Baxter maps. In this work, we construct reflection maps on various geometrical objects, associated with factori
Externí odkaz:
http://arxiv.org/abs/2312.05164
Lagrangian multiforms provide a variational framework to describe integrable hierarchies. The case of Lagrangian $1$-forms covers finite-dimensional integrable systems. We use the theory of Lie dialgebras introduced by Semenov-Tian-Shansky to constru
Externí odkaz:
http://arxiv.org/abs/2307.07339
Publikováno v:
Stud. Appl. Math. 151 (2023), 285-351
The complex coupled short pulse equation (ccSPE) describes the propagation of ultra-short optical pulses in nonlinear birefringent fibers. The system admits a variety of vector soliton solutions: fundamental solitons, fundamental breathers, composite
Externí odkaz:
http://arxiv.org/abs/2210.02265
Publikováno v:
Physica D 445 (2023), 133650
We explore the phenomena of absorption/emission of solitons by an integrable boundary for the nonlinear Schr\"odinger equation on the half-line. This is based on the investigation of time-dependent reflection matrices which satisfy the boundary zero
Externí odkaz:
http://arxiv.org/abs/2206.13978
We describe a variational framework for non-commuting flows, extending the theories of Lagrangian multiforms and pluri-Lagrangian systems, which have gained prominence in recent years as a variational description of integrable systems in the sense of
Externí odkaz:
http://arxiv.org/abs/2204.09663
Publikováno v:
Commun. Math. Phys. 405, 12 (2024)
We cast the classical Yang-Baxter equation (CYBE) in a variational context for the first time, by relating it to the theory of Lagrangian multiforms, a framework designed to capture integrability in a variational fashion. This provides a significant
Externí odkaz:
http://arxiv.org/abs/2201.08286
We perform the analysis of the focusing nonlinear Schr\"odinger equation on the half-line with time-dependent boundary conditions along the lines of the nonlinear method of images with the help of B\"acklund transformations. The difficulty arising fr
Externí odkaz:
http://arxiv.org/abs/2107.02747
Publikováno v:
Lett. Math. Phys. 111, 82 (2021)
We derive the $2$d Zakharov-Mikhailov action from $4$d Chern-Simons theory. This $2$d action is known to produce as equations of motion the flatness condition of a large class of Lax connections of Zakharov-Shabat type, which includes an ultralocal v
Externí odkaz:
http://arxiv.org/abs/2012.04431