Solitary wave solutions of the improved KdV equation by VIM

The variational iteration method (VIM) is applied to solve numerically the improved Korteweg-de Vries equation (IKdV). A correction function is constructed with a general Lagrange multiplier that can be identified optimally via the variational theory. This technique provides a sequence of functions...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-11, Vol.217 (6), p.2397-2403
Main Authors: Hassan, Saleh M., Alotaibi, Naif M.
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Exact solutions
Global analysis, analysis on manifolds
Improved KdV equation
Invariants
Mathematical analysis
Mathematical models
Mathematics
Nonlinear equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Partial differential equations
Sciences and techniques of general use
Solitary waves
Solitons
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Variational iteration method
Wave propagation
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Summary:The variational iteration method (VIM) is applied to solve numerically the improved Korteweg-de Vries equation (IKdV). A correction function is constructed with a general Lagrange multiplier that can be identified optimally via the variational theory. This technique provides a sequence of functions with easily computable components that converge rapidly to the exact solution of the IKdV equation. Propagation of single, interaction of two, and three solitary waves, and also birth of solitons have been discussed. Three invariants of motion have been evaluated to determine the conservation properties of the problem. This procedure is promising for solving other nonlinear equations.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.07.040