Abstract
The generalized KdV equationu 1+auua+μua3+eua5=0[1] is a typical integrable equation. It is derived studying the dissemination of magnet sound wave in cold plasma[2], the isolated wave in transmission line[3], and the isolated wave in the boundary surface of the divided layer fluid[4]. For the characteristic problem of the generalized KdV equation, this paper, based on the Riemann function, designs a suitable structure, then changes the characteristic problem to an equivalent integral and differential equation whose corresponding fixed point, the above integral differential equation has a unique regular solution, so the characteristic problem of the generalized KdV equation has a unique solution. The iteration solution derived from the integral differential equation sequence is uniformly convegent in $$\bar \Omega $$ .
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