Traveling wave solutions (u,v) to a generalized Drinfel’d–Sokolov system which satisfy u=a1vm+a0u=a1vm+a0

An analysis of the coupled generalized Drinfel’d–Sokolov equationsut+α1uux+β1uxxx+γvδx=0andvt+α2uvx+β2vxxx=0is performed in the case of traveling wave solutions u and v   satisfying the condition u=a1vm+a0u=a1vm+a0. We are able to classify all such solutions in terms of the model parameters, and we then discuss the planar dynamics of such solutions. Numerical solutions are obtained and discussed for a variety of parameter regimes. Such results are one possible generalization of those given by Wu et al. [L. Wu, S. Chen, C. Pang, Traveling wave solutions for generalized Drinfeld–Sokolov equations, Applied Mathematical Modeling 33 (2009) 4126–4130].