Approximate explicit solutions of nonlinear BBMB equations by He's methods and comparison with the exact solution

Approximate explicit solution of Camassa-Holm equation by He’s homotopy perturbation method

“…It is a powerful mathematic tool to solve nonlinear problems, especially engineering problems. A lot of authors have used this method to solve many nonlinear differential equations successfully [17,18,[22][23][24][25]. Beside these, HPM is also widely used in engineering [26][27][28][29][30].…”

“…Fortunately, in recent years, a lot of new methods for solving nonlinear ordinary or partial differential equations are developed. For instance, Bäcklund transformation method [1], inverse scattering method [2], Darboux transformation method [3], Adomian's decomposition method [4], Hirota's bilinear method [5], homotopy analysis method [6,7], tanh-function method [8,9], sine-cosine method [10], the bifurcations method of planar dynamical systems [11,12], homotopy perturbation method (HPM) [13][14][15][16][17][18] etc. Generally speaking, all of the above methods have their own advantages and limitations respectively.…”

Application of Homotopy Perturbation Method in Nonlinear Heat Diffusion-Convection-Reaction Equations

“…The calculations were done for two different types of DCRE's such as the Black-Scholes equation used in financial market option pricing, and Fokker-Planck equation from plasma physics. In this work, the basic idea of the HPM is introduced and we extend the analysis of Homotopy perturbation method [5][6][7][8][9][10][11][12][13][14][15] to solve the DCRE equation.…”

“…(1), (5) becomes the approximate solution of Eq. (1) some interesting results have been attained using this method [12][13][14][15][16][17][18].…”

A modified F-expansion method for solving nonlinear pseudoparabolic BBMB equations

“…(1) has been handled by many authors using different mathematical techniques such as El-wakil et al [11] used the exp-function method to obtain the generalized solitary and periodic solutions for eq. (1) [16] applied variational iteration method andhomotopy perturbation method to derive approximate explicit solutions of eq. (1).Gözükizil and Akҫağilsolved eq.…”