View source for The symbolic computation of integrability structures for partial differential equations

<div style="float: right">''Short link  to this page'': [[Symbolic Book|https://gdeq.org/Symbolic_Book]]</div><br>

<div style="float: right">'''[[The symbolic computation of integrability structures for partial differential equations: Errata|Errata]]'''</div>

[[File:Symbolic_Book.jpg|link=http://www.springer.com/gp/book/9783319716541|right|The Springer's page of the book]]

'''Authors''': [[Joseph Krasil'shchik]], [[Alexander Verbovetsky]], and [[Raffaele Vitolo]].

Published in the Springer series [http://www.springer.com/series/3073 Texts and Monographs in Symbolic Computations], 2017. [http://www.springer.com/gp/book/9783319716541 The Springer's page of the book].

''In this book the authors present a unified mathematical approach for the symbolic computation of integrability structures of partial differential equations. By "integrability structures" we mean one of the following: Hamiltonian operators, symplectic operators, recursion operators for symmetries, recursion operators for cosymmetries.''

The computations are carried out within the computer algebra system [http://reduce-algebra.sourceforge.net Reduce] by the packages [[CDE]] and [[CDIFF]].

Many example programs are discussed in the book, [[Media:ISexamples.zip|you can find here a zip file of all examples]].
The examples concern the computation of:
* linearization of a PDE and its adjoint
* higher (or generalized) symmetries
* conservation laws and cosymmetries
* hamiltonian operators
* Schouten bracket of hamiltonian operators (only local operators at the moment)
* symplectic operators (the symplectic property can only be checked for local operators at the moment)
* recursion operators for symmetries
* Nijenhuis tensor of recursion operators for symmetries (only local operators at the moment)
* recursion operatos for cosymmetries.

The above computations are performed for well-known examples of non-linear partial differential equations
in two independent variables, like
* Burgers
* Korteweg-de Vries
* dispersionless Boussinesq
* Camassa-Holm
* Gibbons-Tsarev
* Witten-Dijkgraaf-Verlinde-Verlinde
and in more than two independent variables, like
* Khokhlov-Zabolotskaya
* Kadomtsev-Petviashvili
* Pavlov
* Universal Hyerarchy
* rdDym
* Plebanski
* General Heavenly
* Husain

[[Category:Software|Symbolic Computation]]