Solitary wave solutions and cnoidal wave solutions to the combined KdV and mKdV equation

摘要

AbstractThis paper presents a mapping approach for the construction of exact solutions to the combined KdV and mKdV equation. There exist two types of soliton solutions which will reduce back to those of the KdV and mKdV equations in some appropriate limits. Four types of the general cnoidal wave solutions are also obtained.