# Formal recursion operators of integrable PDEs of the form Utt = F(U,Ux,Ut,...)

Hernández Heredero, Rafael and Caparrós Quintero, Agustín (2017). Formal recursion operators of integrable PDEs of the form Utt = F(U,Ux,Ut,...). In: "FoCM 2017 Foundations of Computational Mathematics Barcelona, July 10th-19th, 2017", 10/07/2017 - 19/07/2017, Barcelona. pp. 124-125.

## Description

Title: Formal recursion operators of integrable PDEs of the form Utt = F(U,Ux,Ut,...) Hernández Heredero, Rafael Caparrós Quintero, Agustín Presentation at Congress or Conference (Speech) FoCM 2017 Foundations of Computational Mathematics Barcelona, July 10th-19th, 2017 10/07/2017 - 19/07/2017 Barcelona 2017 E.T.S.I. y Sistemas de Telecomunicación (UPM) Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones Recognition - No derivative works - Non commercial

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## Abstract

We will explain how the symmetry approach to integrability applies to partial differential equations of the form qtt=F(q,qx,…,qn,qt,qtx,…,qtm). Any such equation is integrable if it admits a formal recursion operator, i.e. a pseudodifferential operator R of the form R:=L+MDt where L and M are pseudodifferential operators in the derivation Dx satisfying the symmetry condition F(L+MDt)=(L+MDt)F... We are confronted with solving an equation over pseudodifferential operators in two derivations, a rather nontrivial problem. The equation happens to have a somewhat triangular structure, making its resolution possible. But in the solving process there appear obstructions, written as conditions over the rhs F of the PDE, that are interpreted as integrability conditions. The algebra of formal recursion operators has an interesting structure, and it has important relationships to algebras of commuting (pseudo)-differential operators in two derivations.

Item ID: 49839 http://oa.upm.es/49839/ oai:oa.upm.es:49839 http://www.ub.edu/focm2017/ Memoria Investigacion 07 Jun 2018 09:42 07 Jun 2018 09:42

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