The solitons and periodic travelling wave solutions for Dodd–Bullough–Mikhailov and Tzitzeica–Dodd–Bullough equations in quantum field theory

Abstract

In this paper, new types of Jacobi elliptic function solutions of Dodd–Bullough–Mikhailov(DBM) and Tzitzeica–Dodd–Bullough(TDB) equations have been obtained using a new extended auxiliary equation method. A new family of explicit travelling wave solutions is derived. The solitary wave solutions and periodic solutions for these equations are formally derived from the Jacobi elliptic function solutions. The proposed method has been efficiently applied to solve the DBM and TDB equations.