Studies Of The Exact Solution In The Plate Equation And The Black-Scholes Equation And Generalization Of Euler Conjecture

In this paper, we first study the symmetry analysis method of the plate equation. We also investigate its invariant group, the optimal system and some exact solutions by using its infinitesimal symmetry.Second, a kind of economic mathematical model which is the Black-Scholes Equation will be researched by the extended C-K direct reduction method, and we get new transform forms of solution.Finally, Euler conjecture which belongs to the ordinary differential equation will be extended to the partial form, and it will be proved by using lie groups analysis. Then we will discuss the application of extended Euler conjecture, and study the four-order rod equation, by this way, we obtain its solutions of Euler conjecture.