Abstract: The generalized KdV equation u_t+auu_s+μu_sℑ+εu_sℑ=0^[1] is a typical integr-able equation. It is derived studying the dissemination of magnet sound wave in coldplasma^[2], Ihe isolated wave in transmission line^[3], and the isolated wave in the bound-ary surface of the divided layer fluid^[4]. For the characteristic problem of the gene-ralized KdV equation, this paper, based on the Riemann function, designs a suitablestructure, then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding fixed point, the above integral differential equ-ation has a unique regular solution, so the characteristic problem of the generalizedKdV equation has a. unique solution. The iteration solution derived from the integraldifferential equation sequence is uniformly convegent in Ω.

Key words: unrestrained, Timoshenko beam, tansverse impact, elastic response, rigid response, momentum, Riemann function, structure, integral and differential equation, fixed point, uniformly convergence