Li Wen-shen. The Uniqueness and Existence of Solution of the Charac-teristic Problem on the Generalized KdV Equation[J]. Applied Mathematics and Mechanics, 1994, 15(5): 463-469.
Citation:
Li Wen-shen. The Uniqueness and Existence of Solution of the Charac-teristic Problem on the Generalized KdV Equation[J]. Applied Mathematics and Mechanics, 1994, 15(5): 463-469.
Li Wen-shen. The Uniqueness and Existence of Solution of the Charac-teristic Problem on the Generalized KdV Equation[J]. Applied Mathematics and Mechanics, 1994, 15(5): 463-469.
Citation:
Li Wen-shen. The Uniqueness and Existence of Solution of the Charac-teristic Problem on the Generalized KdV Equation[J]. Applied Mathematics and Mechanics, 1994, 15(5): 463-469.
The generalized KdV equation ut+αuux+μux3+εux5=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 suitable structure,then changes the characteristic problem to an equivalent integral and dif-ferential equation whose corresponding mapping E is a mapping to itself[5].According to the principle of fixed point,the above integral differential equ-ation 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 Ω .
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