CDE: a Reduce package for integrabilty of PDEs

From Geometry of Differential Equations
Revision as of 00:31, 6 January 2016 by Vitolo (talk | contribs)
Jump to navigation Jump to search

The Reduce package CDE (latest version: 2.0 10/10/2015) is written 'on top' of CDIFF. It is devoted to integrability of general differential equations (i.e., not necessarily in evolution form) with an arbitrary number of dependent and independent variables.

It can compute linearization and adjoints of differential operators in total derivatives, generalized symmetries, conservation laws, Hamiltonian, symplectic and recursion operators, with local and nonlocal coordinates. Schouten brackets between local Hamiltonian operators, also in multidimensions, can be computed. The simplecticity tests for local operators can also be computed. The extension of the Schouten bracket to nonlocal operators is currently under development, as well as symplecticity and hereditariety properties for nonlocal operators. It is distributed under the same free license of REDUCE.

CDE is part of the official Reduce distribution, and can be obtained here, click on the "Download Snapshot" tab and wait a couple of minutes until the server is ready to give you a zip file (about 250MB). However, the distribution is source code and must be compiled; this might be an obstacle for many users. Please do not hesitate to contact the author (use the email raffaele.vitolo@unisalento.it) if you need help. An installable version of Reduce with CDE will be ready in the early days of 2016.

The documentation of CDE is included in the official manual of Reduce; an updated version can be obtained together with the Reduce sources, (same link as above). See inside the /doc folder. The /doc folder also contains documentation for Reduce programming, and in particular the text Inside Reduce, by A.C. Norman and R. Vitolo.

Examples of computations with CDE are contained in the folder /packages/cde/examples of the Reduce sources.

Please feel free to send comments and questions on CDE to the author at raffaele.vitolo@unisalento.it.

In comparison with the previous CDE version 1.0 the new version 2.0 is much faster and more reliable, as it is programmed in Reduce symbolic mode, and has an improved user interface. Moreover it has new features and many new example programs.

The old CDE version 1.0 can still be obtained here.

Retrieved from "https://gdeq.org/index.php?title=CDE:_a_Reduce_package_for_integrabilty_of_PDEs&oldid=3566"