Efficient Iterative Method for Solving Korteweg-de Vries Equations


The Korteweg-de Vries equation plays an important role in fluid physics andapplied mathematics. This equation is a fundamental within study of shallow waterwaves. Since these equations arise in many applications and physical phenomena, itis officially showed that this equation has solitary waves as solutions, TheKorteweg-de Vries equation is utilized to characterize a long waves travelling inchannels. The goal of this paper is to construct the new effective frequent relation toresolve these problems where the semi analytic iterative technique presents newenforcement to solve Korteweg-de Vries equations. The distinctive feature of thismethod is, it can be utilized to get approximate solutions for travelling waves ofnon-linear partial differential equations with small amount of computations does notrequire to calculate restrictive assumptions or transformation like other conventionalmethods. In addition, several examples clarify the relevant features of this presentedmethod, so the results of this study are debated to show that this method is apowerful tool and promising to illustrate the accuracy and efficiency for solvingthese problems. To evaluate the results in the iterative process we used the Matlabsymbolic manipulator.