A different approach for soliton solution of the improved Boussinesq equation

DOI10.1080/00207160310001650053zbMath1076.65088OpenAlexW2072884007MaRDI QIDQ4831403

Mustafa Inc, David J. Evans

Publication date: 29 December 2004

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160310001650053

zbMATH Keywords

convergencenumerical resultsAdomian decomposition methodAdomian polynomialsSolitonthe improved Boussinesq equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (11)

On numerical soliton solution of the Kaup-Kupershmidt equation and convergence analysis of the decomposition method ⋮ A predictor-corrector scheme for the improved Boussinesq equation ⋮ Numerical solutions of the improved boussinesq equation by the galerkin quadratic B-spline finite element method ⋮ A new approach on numerical solutions of the improved Boussinesq type equation using quadratic B-spline Galerkin finite element method ⋮ Numerical study for soliton solutions of some nonlinear evolution equations ⋮ A not-a-knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation ⋮ A second order numerical scheme for the improved Boussinesq equation ⋮ Linear B-spline finite element method for the improved Boussinesq equation ⋮ A comparison between Adomian decomposition and Tau methods ⋮ Quadratic finite volume element method for the improved Boussinesq equation ⋮ On numerical solutions of one-dimensional nonlinear Burgers' equation and convergence of the decomposition method

Uses Software

• Mathematica

Cites Work

• Solving frontier problems of physics: the decomposition method
• Decomposition methods: A new proof of convergence
• A reliable technique for solving the weakly singular second-kind Volterra-type integral equations
• New families of solitons with compact support for Boussinesq-like \(B(m,n)\) equations with fully nonlinear dispersion.
• Approximate solutions to boundary value problems of higher order by the modified decomposition method
• Numerical study of the improved Boussinesq equation
• Nonlinear stability and convergence of finite-difference methods for the good Boussinesq equation
• The solution of the Boussinesq equation using the method of lines
• Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method
• A new formulation of Adomian method
• Numerical Solutions of the Good Boussinesq Equation
• Convergence of Adomian's Method
• Convergence of Adomian's Method and Applications to Non‐linear Partial Differential Equations
• Finite element Galerkin method for the “good” Boussinesq equation
• New numerical study of Adomian method applied to a diffusion model
• On the solution of the fourth order parabolic equation by the decomposition method
• A review of the decomposition method and some recent results for nonlinear equations
• Explicit solutions of generalized nonlinear Boussinesq equations

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