Abstract
The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of non-linear partial differential equations with small amount of computations does not require to calculate restrictive assumptions or transformation like other conventional methods. In addition, several examples clarify the relevant features of this presented method, so the results of this study are debated to show that this method is a powerful tool and promising to illustrate the accuracy and efficiency for solving these problems. To evaluate the results in the iterative process we used the Matlab symbolic manipulator.
Highlights
In the previous few decades, Non-linear phenomena play an important tool in physics, the solitary wave theory and applied mathematics
The study of non-linear partial differential equations in modelling physical phenomena become a significant gadget in a large class and vastly utilized in assorted fields of the nonlinear natural sciences, As for the behavior and properties of nonlinear partial differential equations can be determined by exact solution ; non-linear equations play significant role in specifying such problems
These solutions come accurate and in agreement with the exact solution provided by analytical results
Summary
In the previous few decades, Non-linear phenomena play an important tool in physics, the solitary wave theory and applied mathematics. To the best of our knowledge, SAIM is not yet implemented to resolve the KdV equations This method can be used to solve and get the analytical solutions of these problems. ADM had be utilized to solve the KdV equation to get a solitary wave solution, the Modified Adomian Decomposition Method(MADM) used to solve non-linear dispersive waves via Boussinesq equation, [29]. Step (3) : After several simple iterative steps of the solution, the general form of this equation which is Solving this equation and integrating both sides of Eq(2.12) from 0 to t, leads to obtain ( ). This method has merit to solve and apply KdV equation
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