Regular ArticleThe Boundary Forced MKdV Equation
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Numerical investigations of shallow water waves via generalized equal width (GEW) equation
2021, Applied Numerical MathematicsStudy on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm
2020, Mathematics and Computers in SimulationCitation Excerpt :Researchers used different analytical and numerical techniques for the solution of KdV equation (1) like Wang H, and Xiang C. [48] used Jacobi elliptic periodic function transform technique, Bakodah et al. [5] employed Adomian decomposition method based on convergence parameter, Syam [46] used Adomian decomposition method, Lakestani [20] has used B-Spline Functions, Korkmaz [18] has utilized cosine expansion based differential quadrature methods, El-Wakil et al. [7] have used computerized technique using symbolic computation, Abbassbanday and Zakaria [1] used homotopy analysis method, Chebyshev spectral method has been used by Helal [13], Seadawy [30] employed variational approximation method for explicit solutions as well as the direct algebraic method [31] of different types of KdV equations, while variational iteration method was employed by Wazwaz [49]. Many authors have solved equation (2) by different techniques like Geyikli and Kaya [11] employed both the finite element and the decomposition methods, Gardner et al. [10] utilized the B-spline finite element technique, El-Wakil et al. [7] has used computerized technique using symbolic computation, Shoucri et al. [44] used shape-preserving splines, Fontenelle et al. [9] presented recurrence relations for generating the terms for densities, Iqbal et al. [15] used direct algebraic method with new modification, while Mokhtari and Mohseni [24] have used meshless method based on global collocation using RBF, direct algebraic method, extended mapping method and Seadawy techniques [26,34–36,40–42]. To solve the model (3) numerically several methods can be found in the literature like Bakodah et al. [5] employed Adomian decomposition method based on convergence parameter, the direct method and leading order analysis technique were used by Zhang [51], Lu and Shi [21] have used Jacobi elliptic functions expansion method, modified functional variable method has been utilized by Djoudi and Zerarka [6], Kaya and Inan [16] employed decomposition method, an effective homogeneous balance method is used by Yu [50], unified algebraic method used by Fan [8], Seadawy and Rashidy [37] used a transformation method, while extended mapping method has been used by Krishnan and Peng [19].
Analytical and computational approaches on solitary wave solutions of the generalized equal width equation
2020, Applied Mathematics and ComputationA meshless method for solving mKdV equation
2012, Computer Physics CommunicationsCitation Excerpt :They studied it because of its relevance to plasma physics, as well as to the Fermi–Pasta–Ulam puzzle [6]. Some theoretical and numerical studies of mKdV equation, among other places, have appeared in the literature [7–12]. Moreover, many analytical methods have been reported in [15].
Solitary waves induced by the boundary forced EW equation
2001, Computer Methods in Applied Mechanics and EngineeringSolitary wave interactions for the modified equal width equation
2000, Computer Physics Communications