Imperial College London
Alternate

DrAlexisArnaudon

Faculty of Natural Sciences, Department of Mathematics

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Contact

 

+44 (0)7463 328 499alexis.arnaudon Website

 
 
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Location

 

6M34Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Arnaudon:2016:10.1007/s00332-016-9300-2,
author = {Arnaudon, A},
doi = {10.1007/s00332-016-9300-2},
journal = {Journal of Nonlinear Science},
pages = {1133--1160},
title = {On a lagrangian reduction and a deformation of completely integrable systems},
url = {http://dx.doi.org/10.1007/s00332-016-9300-2},
volume = {26},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We develop a theory of Lagrangian reduction on loop groups for completely integrable systems after having exchanged the role of the space and time variables in the multi-time interpretation of integrable hierarchies. We then insert the Sobolev norm H1H1 in the Lagrangian and derive a deformation of the corresponding hierarchies. The integrability of the deformed equations is altered, and a notion of weak integrability is introduced. We implement this scheme in the AKNS and SO(3) hierarchies and obtain known and new equations. Among them, we found two important equations, the Camassa–Holm equation, viewed as a deformation of the KdV equation, and a deformation of the NLS equation.
AU  - Arnaudon,A
DO  - 10.1007/s00332-016-9300-2
EP  - 1160
PY  - 2016///
SN  - 1432-1467
SP  - 1133
TI  - On a lagrangian reduction and a deformation of completely integrable systems
T2  - Journal of Nonlinear Science
UR  - http://dx.doi.org/10.1007/s00332-016-9300-2
UR  - http://hdl.handle.net/10044/1/33398
VL  - 26
ER  -
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