The optimal homotopy-analysis method for Kawahara equation

DOI10.1016/j.nonrwa.2010.10.013zbMath1213.35030OpenAlexW1990104254MaRDI QIDQ533045

Qi Wang

Publication date: 2 May 2011

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2010.10.013

zbMATH Keywords

auxiliary convergence-control parameters

Mathematics Subject Classification ID

Other special methods applied to PDEs (35A25) Traveling wave solutions (35C07)

Related Items (13)

New exact solutions for the space-time fractional Kawahara equation ⋮ Approximate solutions of time fractional Kawahara equation by utilizing the residual power series method ⋮ Finding optimal convergence control parameter in the homotopy analysis method to solve integral equations based on the stochastic arithmetic ⋮ Heat transfer analysis of Williamson fluid over exponentially stretching surface ⋮ Conservative compact difference scheme based on the scalar auxiliary variable method for the generalized Kawahara equation ⋮ Predictor homotopy analysis method: two points second order boundary value problems ⋮ Unique and multiple PHAM series solutions of a class of nonlinear reactive transport model ⋮ New analytical method for gas dynamics equation arising in shock fronts ⋮ An analytic solution for the space-time fractional advection-dispersion equation using the optimal homotopy asymptotic method ⋮ Application of Adomian decomposition method to nonlinear systems ⋮ Numerical approximation of modified Kawahara equation using kernel smoothing method ⋮ An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials ⋮ Stable soliton solutions to the shallow water waves and ion-acoustic waves in a plasma

Cites Work

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• A numerical comparison of a Kawahara equation
• Notes on the homotopy analysis method: some definitions and theorems
• An optimal homotopy-analysis approach for strongly nonlinear differential equations
• New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations
• An explicit, totally analytic approximate solution for Blasius' viscous flow problems
• Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine-Cosine method
• The application of homotopy analysis method to nonlinear equations arising in heat transfer
• Homotopy analysis method for the Kawahara equation
• A kind of approximation solution technique which does not depend upon small parameters. II: An application in fluid mechanics
• New exact travelling wave solutions for the Kawahara and modified Kawahara equations
• An approximate solution technique not depending on small parameters: A special example
• The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation

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