The investigation of exact solutions for the appropriate type of the dispersive long wave equation (Q1653885)

Summary: Improved \((G'/G)\)-expansion and first integral methods are used to construct exact solutions of the \((2+1)\)-dimensional Eckhaus-type extension of the dispersive long wave equation. The \((G'/G)\)-expansion method is based on the assumptions that the travelling wave solutions can be expressed by a polynomial in \((G'/G)\) and the first integral method is based on the theory of commutative algebra in which Division Theorem is of concern. It is worth mentioning that these methods are used for different systems and those two different systems can both be reduced to a system that will be mentioned in this paper. To recapitulate, this investigation has resulted in the exact solutions of the given systems.