Exact two waves solutions with variable amplitude to the KdV equation

Abstract

By means of the Darboux transformation method, a series of explicit variable amplitude-two-wave solutions to the Korteweg-de Vries (KdV) equation are generated from a particular solution with respect to the independent variable x. Theses new solutions include single soliton solutions, two-soliton solutions, single periodic solutions, doubly periodic solutions. Mathematics Subjection Classification: 35Q51; 35A