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
- 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/).
Cite this article
TY - JOUR AU - Anahita Eslami Rad AU - Jean-Pierre Magnot AU - Enrique G. Reyes PY - 2021 DA - 2021/01/06 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 - 10.1080/14029251.2017.1418057 ID - Rad2021 ER -