CDE: a Reduce package for integrabilty of PDEs
The Reduce package CDE (latest version: 2.0 10/10/2015) is written 'on top' of CDIFF. It is devoted to computations on quantities which are related with the 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 extension of the Schouten bracket to nonlocal operators is currently under development, as well as symplecticity and hereditariety properties. It is distributed under the same free license of REDUCE.
In comparision 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, like the computation of linearization and its adjoint, and new examples programs.
The above zip file contains:
- A README.txt file;
- The program file cde.red, for computations of differential consequences of even and odd partial differential equations and of the related total derivatives.
- The file Cde-userguide-2.0.pdf, a CDE 2.0 user guide for computations of generalized symmetries, conservation laws, Hamiltonian, symplectic and recursion operators, in local and nonlocal coordinates.
- The file global.txt with a list of global variables used in cde.red.
- The folder examples, which contains all examples described in the user guide with results and debug files.
The author of the package, Raffaele Vitolo, welcomes comments and questions on CDE (use the email raffaele.vitolo@unisalento.it).
The old CDE version 1.0 can still be obtained here.