Development of Symbolic Software for Nonlinear Partial Differential Equations

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9300978 Hereman This project deals with the development and implementation of new symbolic algorithms for the computation of Lie symmetries, the investigation of integrability, and the calculation of exact solutions of systems of nonlinear partial differential equations (PDEs). The first symbolic program will assist in computing classical and nonclassical Lie-point symmetries, as well as generalized symmetries, for large systems of differential equations. The second software package will automatically carry out the Painleve integrability test for the existence of soliton solutions. Via a unified bilinear transformation method, it will create 'solitons' for a large class of integrable PDEs. The development of novel mathematical techniques, in addition to the refinement and generalization of existing methods, is an essential part of this research project. The goal is to provide high quality symbolic programs, in MACSYMA and MATHEMATICA, to researchers working on soliton theory, dynamical systems, mathematical physics; specifically wave phenomena in meteorology, bio-sciences, fluid dynamics, plasma and particle physics, and nonlinear optics. ***