Development of Symbolic Software for Nonlinear Partial Differential Equations

9300978 Hereman该项目涉及新的符号算法的开发和实现，用于计算Lie对称性，可积性的研究以及非线性偏微分方程（PDE）系统的精确解的计算。 第一个符号程序将帮助计算经典和非经典的李点对称性，以及广义对称性，为大型系统的微分方程。 第二个软件包将自动进行Painleve可积性测试的存在孤子解决方案。 通过一个统一的双线性变换方法，它将创建一个大类的可积偏微分方程的“孤子”。 新的数学技术的发展，除了现有方法的细化和推广，是这个研究项目的重要组成部分。 其目标是提供高质量的符号程序，在MACSYMA和MATHEMATICA，研究孤子理论，动力系统，数学物理工作;特别是在气象学，生物科学，流体动力学，等离子体和粒子物理，非线性光学的波动现象。 ***

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. ***