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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/916793 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841524845996670976 |
|---|---|
| author | Ji-Huan He |
| author_facet | Ji-Huan He |
| author_sort | Ji-Huan He |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3eb798af48a54ea1902569de5de1a7b6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3eb798af48a54ea1902569de5de1a7b62025-02-03T05:47:15ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/916793916793Asymptotic Methods for Solitary Solutions and CompactonsJi-Huan He0National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Renai Road, Suzhou 215123, ChinaThis 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.http://dx.doi.org/10.1155/2012/916793 |
| spellingShingle | Ji-Huan He Asymptotic Methods for Solitary Solutions and Compactons Abstract and Applied Analysis |
| title | Asymptotic Methods for Solitary Solutions and Compactons |
| title_full | Asymptotic Methods for Solitary Solutions and Compactons |
| title_fullStr | Asymptotic Methods for Solitary Solutions and Compactons |
| title_full_unstemmed | Asymptotic Methods for Solitary Solutions and Compactons |
| title_short | Asymptotic Methods for Solitary Solutions and Compactons |
| title_sort | asymptotic methods for solitary solutions and compactons |
| url | http://dx.doi.org/10.1155/2012/916793 |
| work_keys_str_mv | AT jihuanhe asymptoticmethodsforsolitarysolutionsandcompactons |