McCowan's Solitary Wave Expansions

摘要

In 1894 McCowan proposed that the structure of solitary waves be represented by a certain series expansion; but he gave an estimate for only the first term of this expansion. Any truncation of such an expansion compromises the essential ideal of the steadiness of a solitary wave; also, the approximations which he adopted might not be the best ones for the diverse particular purposes for which this wave may be used. In the paper a more precise structure of this wave is constructed by implementing McCowan's expansion to higher orders. The coefficients in this expansion are determined by minimizing a certain reasonable measure of the imperfection of this expansion. This minimization is done by using the FNMIN subroutine. (Author)