Cylindrical korteweg-de vries equation and travelling wave solutions

摘要

The power cylindrical Korteweg-de Vries equation, u_η + u_2η+u~nuξ+uξξξ=0, is considered. The author transforms this equation into the power Kadomtsev-Petviashvili equation. Solitary wave solutions and cnoidal wave solutions are obtained. The cnoidal wave solutions re shown to be representable as infinite sums of solitons by using Fourier series expansion and Poisson's summation formula.