Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System

Abstract

Abstract Nonlinear Drinfeld-Sokolov system is studied analytically by using four different methods ((G′/G)-expansion, direct algebraic, different form of the (G′/G)-expansion methods, and direct integration) and the results are found numerically. New exact and numeric solutions are given and the comparison of the results obtained from these different methods, methods themselves and numerical results are discussed in detail. It is found that the (G′/G)-expansion and different form of the (G′/G)-expansion methods are really coincide and effective methods in the view of finding different solutions that cannot be obtained by using the direct integration for Drinfel-Sokolov system.