Solitary-wave solutions of the Degasperis–Procesi equation by means of the homotopy analysis method

Abbasbandy, Saeid; Parkes, E.J.

doi:10.1080/00207160802626492

Cited by 9 publications

(6 citation statements)

References 26 publications

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“…Unlike perturbative and non‐perturbative methods it also gives us huge freedom to choose the proper initial guesses and the linear operators to approximate nonlinear problems. This method has already been successfully applied by several researchers to various interesting problems in science and engineering [25–31].…”

Section: Computations Of Solutions By Homotopy Analysis Methods (Ham)mentioning

confidence: 99%

Boundary layer flow of an Oldroyd‐B fluid with convective boundary conditions

Hayat

Iqbal

Mustafa

et al. 2011

Heat Trans. Asian Res.

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This study is presented for the flow of an Oldroyd-B fluid subject to convective boundary conditions. The two-dimensional equations are simplified by using boundary layer approximations. The analytic solutions in the whole spatial domain (0 ≤ η < ∞) are derived by a homotopy analysis method (HAM). Interpretation of various emerging parameters is assigned through graphs for velocity and temperature distributions and tables for surface heat transfer. The present results are compared with the previous studies in limiting cases and results are found in very good agreement.

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Section: Computations Of Solutions By Homotopy Analysis Methods (Ham)mentioning

confidence: 99%

Boundary layer flow of an Oldroyd‐B fluid with convective boundary conditions

Hayat

Iqbal

Mustafa

et al. 2011

Heat Trans. Asian Res.

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“…More recently developed techniques that make use of computer algebra software include the simplest equation method and its extensions [ 15 , 17 ], the equivalent -extension and tanh-extension methods [ 16 , 40 ], and the homotopy analysis method [ 1 ]. A novel adaptation of the -expansion technique is used to construct solitary wave solutions to the dimensional Konopelchenko–Dubrovsky and Kadomtsev–Petviashvili equations in [ 5 ].…”

Section: Introductionmentioning

confidence: 99%

Higher order solitary solutions to the meta-model of diffusively coupled Lotka–Volterra systems

et al. 2021

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A meta-model of diffusively coupled Lotka–Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of nth order solitary solutions are derived via a modified inverse balancing technique. It is shown that as the highest possible solitary solution order n is increased, the number of nonzero solution parameter values remains constant for solitary solutions of order $n>3$ n > 3 . Analytical and computational experiments are used to illustrate the obtained results.

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“…Probably the first papers where HAM was applied to the study of nonlinear waves were [31,32], in which solutions to the problem of progressive waves in deep water and solutions for periodic waves for the mKDV equation, respectively, were derived. Ever since, HAM has been successfully applied to obtain soliton and/or peakon solutions of various important nonlinear PDEs including but not limited to the Fitzhugh-Nagumo equation [33], the CH equation [34,35], a 5th order KdV equation [36], and the DP equation [37,38].…”

Section: Introductionmentioning

confidence: 99%