The Cauchy problem of the Kadomtsev-Petviashvili hierarchy with arbitrary coefficient algebra
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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.
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
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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 -