Abstract
We present a simple and effective transformation that decompose the solution of a coupled system into solving a set of algebraic equations and a first order ordinary differential equation of a certain unknown function. This method not only gives us a clear relation between unknown functions for a nonlinear coupled system, but also easily provides us with a series of new and more general travelling wave solutions in terms of special functions such as hyperbolic, rational, triangular, Weierstrass and Jacobi elliptic double periodic functions.
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