A set of exact and explicit solitary wave solutions for a class of generalized KdV equations with arbitrary odd order derivatives (A sieving method in a closed function class)

Abstract

Recent higher order KdV equations are interesting for physics, for example when the surface tension approaches close to a certain value. In this paper using the method of sieving in a closed function class, a set of exact and explicit solitary wave solutions with a unified form are given to higher order or generalized higher order KdV equations with 7th, 9th or arbitrary odd order derivatives, when their parameters satisfy some suitable restricted conditions.