Asymptotic Methods for Solitary Solutions and Compactons

This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to gi...

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Published inAbstract and Applied Analysis Vol. 2012; no. 1; pp. 727 - 856-748
Main Author He, Ji-Huan
Format Journal Article
LanguageEnglish
Published New York Hindawi Limiteds 01.01.2012
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Wiley
Subjects
Canals
Methods
Partial differential equations
Studies
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Summary:This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/916793