الفهرس | Only 14 pages are availabe for public view |
Abstract Hidden symmetries of non linear differential equations are here investigated. These symmetries were defined in the early nineties by Barbara Shrauner [1-5] for problems having no Lie vectors or no closed form solution. The subject was then left dormant for twenty years. We in this thesis track the hidden syrnmetries, type I and type II for nonlinear ordinary and partial differential equations using Lie extended differential method. Then for highly non linear partial differential equations construct of an optimal set of Lie vectors [6] and explore its hidden syrnmetries. Using these vectors we reduce the partial differential equations to ordinary ones, sometimes to a fourth reduction level, tracking hidden symmetries. For each application analytical solutions were obtained and algebraic rules were deducted. These rules are new and will help future workers in the field. For each analytical solution a comparison was done whenever available with the most of recent researches. Many of the obtained new solutions appear III real life. |