Adomian decomposition method for approximating the solution of the Korteweg-deVries equa\-tion

DOI10.1016/j.amc.2004.03.021zbMath1063.65112OpenAlexW2013289057MaRDI QIDQ1765879

Muhammed I. Syam

Publication date: 23 February 2005

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2004.03.021

zbMATH Keywords

Adomian decomposition methodKorteweg-deVries equationAdomian polynomialsNumerical examplesInitial value problem

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Analytic solution for a nonlinear problem of magneto-thermoelasticity ⋮ Solitary wave solutions of the improved KdV equation by VIM ⋮ Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method ⋮ Eventual periodicity of forced oscillations of the Korteweg-de Vries type equation ⋮ A novel method for solving KdV equation based on reproducing kernel Hilbert space method ⋮ Breather and solitons waves in optical fibers via exponential time differencing method ⋮ Sine-cosine method for finding the soliton solutions of the generalized fifth-order nonlinear equation ⋮ Efficient shooting method for solving two point boundary value problems ⋮ Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm ⋮ A reliable technique for solving third‐order dispersion equations ⋮ A modification of the Adomian decomposition method for a class of nonlinear singular boundary value problems ⋮ A comparative study of numerical methods for solving the generalized Ito system ⋮ Weighted residual method for obtaining positive solutions of two-point nonlinear boundary value problems ⋮ An efficient method for analyzing the solutions of the Korteweg-de Vries equation ⋮ Numerical solution of singularly perturbed fifth order two point boundary value problem

Cites Work

• A review of the decomposition method in applied mathematics
• A comparison between Adomian decomposition method and Taylor series method in the series solutions
• Solving frontier problems of physics: the decomposition method
• Method of lines solution of the Korteweg-de Vries equation
• Distinct variants of the KdV equation with compact and noncompact structures.
• Compact structures for variants of the generalized KdV and the generalized KP equations.
• Compactons, solitons and periodic solutions for variants of the KdV and the KP equations
• A new modification of the Adomian decomposition method for linear and nonlinear operators
• A Simple Derivation of the N-Soliton Solutions to the Korteweg--deVries Equation
• Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation

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