Cylindrical and spherical Korteweg–deVries solitary waves

Abstract

Solitary wave solutions for the dimensionally modified Korteweg–deVries equation appropriate to symmetric ion acoustic waves in both cylindrical and spherical geometrics are presented. Expressions are given for the amplitude, velocity, width, and energy. The energy in the main body of the solitary wave continually decreases due to energy transfer to the trailing structure. The solutions are verified by comparison with a numerical integration of the differential equation.