Abstract
In this study, we used Double Elzaki Transform (DET) coupled with Adomian polynomial to produce a new method to solve Third Order Korteweg-De Vries Equations (KdV) equations. We will provide the necessary explanation for this method with addition some examples to demonstrate the effectiveness of this method.
Highlights
Open Access tial differential equation, well known by the Korteweg-de Vries (KdV) equation, to model the height of the surface of shallow water in the presence of solitary wave’s
The KdV equation describes the propagation of plasma waves in a dispersive medium
We study a new method to solutions of KdV equations namely Double Elzaki Transform Decomposition Method (DETDM), this method is its capability of combining easy integral transform Double ELzaki Transform (DET) [8] and an effective method for solving non-linear partial differential equations, namely Adomian Decomposition Method [1]
Summary
Open Access tial differential equation, well known by the Korteweg-de Vries (KdV) equation, to model the height of the surface of shallow water in the presence of solitary wave’s. Double Elzaki Transform, Adomian Polynomial, Korteweg-De Vries Equations Third order Korteweg-de-Vries (KdV) equation of the form ut + auux + buxxx = 0 (1) Definition: Let f ( x,t ),t, x ∈ R+ be a function which can be expressed as a convergent infinite series, its Double Elzaki Transform given by: E2 f ( x,t )= ,u, v
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