The Symbolic Computation of Integrability Structures for Partial Differential Equations

Joseph Krasil'shchik is a principal researcher at the Institute of Control Sciences of Russian Academy of Sciences and a full professor at the Independent University of Moscow. Alexander Verbovetsky is a lecturer at the Independent University of Moscow. Raffaele Vitolo is an associate professor in mathematical physics at the Department of Mathematics and Physics 'E. De Giorgi' of the Università del Salento.

Introduction.- Computational problems in the geometry of PDEs.- Old and new Reduce software for integrability of PDEs.- Internal coordinates and total derivatives.- Conservation laws and nonlocal variables.- Cosymmetries.- Symmetries.- The tangent covering.- Recursion operators for symmetries.- Variational symplectic structures.- Cotangent covering.- Variational Poisson structures.- Recursion operators for cosymmetries.- The Plebanski equation.- Discussion.