The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation

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On convergence of homotopy analysis method and its application to fractional integro-differential equations (2013, methodology): “Recently, HAM has been successfully applied to some special equations like the generalized Hirota-Satsuma coupled KdV (Korteweg-de Vries) equation [1], the thin film flow [31], the generalized Zakharov equation [3], MHD (Magnetohydrodynamics) Falkner-Skan flow [4], micropolar fluid [29], pipe flow o”
An explicit solution of the large deformation of a cantilever beam under point load at the free tip (2008, neutral): “... Define the exact solution by means of solving Eq. (10) **********************************************************************************) Exact[ z_ ] :=Module[{ temp, k, eq, phi }, k = (1 + Sin[ x ] )/2; phi = ArcSin[1 / Sqrt [2*k] ]; eq = EllipticK[ k ] − EllipticF[ phi, k ] − Sqrt[ z ]; temp[”
A General Approach to Obtain Series Solutions of Nonlinear Differential Equations (2007, methodology): “The homotopy analysis method has been successfully applied to many nonlinear problems in science and engineering, such as the similarity boundary-layer flows [27, 37‐39], nonlinear heat transfer [40, 33, 35], nonlinear evaluation equations [41], nonlinear waves [ 34 ], viscous flows of non-Newtonian”