On numerical soliton solution of the Kaup-Kupershmidt equation and convergence analysis of the decomposition method

DOI10.1016/j.amc.2005.01.120zbMath1088.65089OpenAlexW4236619748MaRDI QIDQ2369069

Yanyan Li

Publication date: 28 April 2006

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

Full work available at URL: https://doi.org/10.1016/j.amc.2005.01.120

zbMATH Keywords

convergencenumerical examplessolitonAdomian decomposition methodnonlinear evolution equationKaup-Kupershmidt equationSawada-Kotera equationAdomian polynomials

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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)

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Uses Software

• Mathematica

Cites Work

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• Symbolic methods to construct exact solutions of nonlinear partial differential equations
• Solitons and infinite dimensional Lie algebras
• Two integrable differential-difference equations exhibiting soliton solutions of the Kaup-Kupershmidt equation type
• Solving frontier problems of physics: the decomposition method
• Convergence of Adomian's method applied to differential equations
• An explicit and numerical solutions of some fifth-order KdV equation by decomposition method
• Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics
• An application of the decomposition method for the generalized KdV and RLW equations
• A new algorithm for calculating Adomian polynomials for nonlinear operators
• Nonlinear superposition formula for the Kaup-Kuperschmidt partial differential equation
• Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method
• Practical formulae for the calculus of multivariable Adomian polynomials
• Non-autonomous Hénon-Heiles systems
• On soliton solutions of the Kaup-Kupershmidt equation. I: Direct bilinearisation and solitary wave
• On soliton solutions of the Kaup-Kupershmidt equation. II: `Anomalous' \(N\)-soliton solutions
• On numerical solutions of one-dimensional nonlinear Burgers' equation and convergence of the decomposition method
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• The prolongation structure of a higher order Korteweg-de Vries equation
• Convergence of Adomian’s method applied to integral equations
• The Decomposition Method For Solving Of A Class Of Singular Two-Point Boundary Value Problems
• New numerical study of Adomian method applied to a diffusion model
• A new approach to solve a diffusion‐convection problem
• A different approach for soliton solution of the improved Boussinesq equation
• Integrals of nonlinear equations of evolution and solitary waves