Vladimir P. Gerdt
(gerdt@jinr.dubna.su)
Laboratory of Computing Techniques and Automation
Joint Institute for Nuclear Research
141980 Dubna
RUSSIA
Tel: (7-09621) 63437
Fax: (7-09621) 65145
The session is to be devoted to the algorithmic and applied aspects of analysis of algebraic PDEs, based on their transformation into the special forms which are called in the literature as formal integrable, passive, involutive or standard. Such forms are much like to a Groebner basis and allow one to extract an important information on the equation system without its explicit integration. This information includes, in particular, compatibility analysis, finding dimension of the solution space, formulation of the initial conditions providing uniqueness and holomorphy of solution. Recently a number of different algorithmic techniques were designed and some of them have been implemented in computer algebra systems Axiom, Maple and Reduce. Over the session one expects presentation of some algorithmic approaches and their discussion in view of differential algebra, interconnection of the above special forms of PDEs with differential Groebner bases and characteristic sets, application to real problems of theoretical and mathematical physics, applied mathematics. One of the most important applications is Lie symmetry analysis of nonlinear differential equations which is the most universal tool of their integration.
