Journal of Nonlinear Mathematical Physics

Volume 24, Issue Supplement 1, December 2017, Pages 103 - 120

The Cauchy problem of the Kadomtsev-Petviashvili hierarchy with arbitrary coefficient algebra

Authors
Anahita Eslami Rad
Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile. anahita.eslami@usach.cl
Jean-Pierre Magnot
LAREMA, Universit d’Angers, 2 Bd Lavoisier, 49045 Angers cedex 1, France
Lycée Jeanne d’Arc, Avenue de Grande Bretagne, 63000 Clermont-Ferrand, France. jean-pierr.magnot@ac-clermont.fr
Enrique G. Reyes
Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile, enrique.reyes@usach.cl, e_g_reyes@yahoo.ca
Received 18 September 2017, Accepted 13 November 2017, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2017.1418057How to use a DOI?
Abstract

Mulase solved the Cauchy problem of the Kadomtsev-Petviashvili (KP) hierarchy in an algebraic category in “Solvability of the super KP equation and a generalization of the Birkhoff decomposition” (Inventiones Mathematicae, 1988), making use of a delicate factorization of an infinite-dimensional group of formal pseudodifferential operators of infinite order. We prove Mulase’s factorization theorem in a smooth category in the setting of formal pseudo-differential operators with coefficients in a (non-commutative) algebra equipped with a valuation. As an application, we solve the initial value problem for the KP hierarchy using r-matrix theory.

Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - Supplement 1
Pages
103 - 120
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2017.1418057How to use a DOI?
Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Anahita Eslami Rad
AU  - Jean-Pierre Magnot
AU  - Enrique G. Reyes
PY  - 2021
DA  - 2021/01
TI  - The Cauchy problem of the Kadomtsev-Petviashvili hierarchy with arbitrary coefficient algebra
JO  - Journal of Nonlinear Mathematical Physics
SP  - 103
EP  - 120
VL  - 24
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1418057
DO  - https://doi.org/10.1080/14029251.2017.1418057
ID  - Rad2021
ER  -