Travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov (D(m,n)D(m,n)) system

In this paper, travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov system (called D(m,n)D(m,n) system) are studied by using the Weierstrass elliptic function method. As a result, more new exact travelling wave solutions to the D(m,n)D(m,n) system are obtained including not only all the known solutions found by Xie and Yan but also other more general solutions for different parameters m,nm,n. Moreover, it is also shown that the D(m,1)D(m,1) system with linear dispersion possess compacton and solitary pattern solutions. Besides that, it should be pointed out that the approach is direct and easily carried out without the aid of mathematical software if compared with other traditional methods. We believe that the method can be widely applied to other similar types of nonlinear partial differential equations (PDEs) or systems in mathematical physics.