KdV—Benjamin—Ono方程的初值与线性化问题的准确解

本文证明了KdV—Benjamin—Ono方程初值问题解的唯一性与稳定性;借助于Fourier变换求出了线性化的KdV—Benjamm—Ono方程初值问题的准确解,即积分表达式。当初值函数充分光滑并且在无穷远处充分快地趋于零时。证明了问题的古典解存在。

The Initial Value Problem for KdV—Benjamin—Ono Equation and the Exact Solution to the Linearized problem

In the present paper, the uniqueness and stability of the solution to the initial value problem of the kdV—Benjamin—Ono equation is proved. The exact solution, i. e. , the integral representation of the solution to the initial value problem of the linearized kdV—B—O equation is given by means of Fouries Transform. If the initial value function and Its derivatives approach to zero rapidly as |x|→∞, there exists the classical solution to the problem.