Semianalytical Methods for Solving the KdV and mKdV Equations
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Glosarry
 Adomian decomposition method, homotopy analysis method, homotopy perturbation method, and variational perturbation method

These are some of the semianalytical/numerical methods for solving Ordinary Differential Equation (in short ODE) or Partial Differential Equation (in short PDE) in literature. – Exact solution A solution to a problem that contains the entire physics and mathematics of a problem, as opposed to one that is approximate, perturbative, closed, etc. – Kortewegde Vries equation The classical nonlinear equations of interest usually admit for the existence of a special type of the traveling wave solutions, which are either solitary waves or solitons. – Modified Kortewegde Vries This equation is a modified form of the classical KdV equation in the nonlinear term. – Soliton This concept can be regarded as solutions of nonlinear partial differential equations.
Definition of the Subject
In this study, some semianalytical/numerical methods are applied to solve the...
Bibliography
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Books and Reviews
 The following, referenced by the end of the paper, is intended to give some useful for further readingGoogle Scholar
 For another obtaining of the KdV equation for water waves, see Kevorkian and Cole (1981); one can see the work of the Johnson (1972) for a different waterwave application with variable depth, for waves on arbitrary shears in the work of Freeman and Johnson (1970) and Johnson (1980) for a review of one and twodimensional KdV equations. In addition to these; one can see the book of Drazin and Johnson (1989) for some numerical solutions of nonlinear evolution equations. In the work of the Zabusky, Kruskal and Deam (F1965) and Eilbeck (F1981), one can see the motion pictures of soliton interactions. See a comparison of the KdV equation with water wave experiments in Hammack and Segur (1974)Google Scholar
 For further reading of the classical exact solutions of the nonlinear equations can be seen in the works: the Lax approach is described in Lax (1968); Calogero and Degasperis (1982, A.20), the Hirota’s bilinear approach is developed in Matsuno (1984), the Bäckland transformations are described in Rogers and Shadwick (1982); Lamb (1980, Chap. 8), the Painleve properties is discussed by Ablowitz and Segur (1981, Sect. 3.8), In the book of Dodd, Eilbeck, Gibbon and Morris (1982, Chap. 10) can found review of the many numerical methods to solve nonlinear evolution equations and shown many of their solutionsGoogle Scholar