The Local Well-posedness For The Boussinesq Equation With Quasi-period Initial Data

This paper studies the local well-posedness for the "good" Boussinesq equation.We prove that the Fourier coefficient of the solution for the "good" Boussinesq equa-tion is exponentially decaying by constructing iterative program under the condition of quasi-period initial data and the solution is unique in a short period of time.In addition,the length of time of the solution depends on the given initial value and frequency vector involved.