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,...)
Author/s:
  • Hernández Heredero, Rafael
  • Caparrós Quintero, Agustín
Item Type: Presentation at Congress or Conference (Speech)
Event Title: FoCM 2017 Foundations of Computational Mathematics Barcelona, July 10th-19th, 2017
Event Dates: 10/07/2017 - 19/07/2017
Event Location: Barcelona
Date: 2017
Subjects:
Faculty: E.T.S.I. y Sistemas de Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

Full text

[img]
Preview
PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (266kB) | Preview

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.

More information

Item ID: 49839
DC Identifier: http://oa.upm.es/49839/
OAI Identifier: oai:oa.upm.es:49839
Official URL: http://www.ub.edu/focm2017/
Deposited by: Memoria Investigacion
Deposited on: 07 Jun 2018 09:42
Last Modified: 07 Jun 2018 09:42
  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM