A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results
This paper is focused on studying approximate damped oscillatory solutions of the compound KdV-Burgers-type equation with nonlinear terms of any order. By the theory and method of planar dynamical systems, existence conditions and number of bounded traveling wave solutions including damped oscillato...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/935915 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556942827978752 |
|---|---|
| author | Yan Zhao Weiguo Zhang |
| author_facet | Yan Zhao Weiguo Zhang |
| author_sort | Yan Zhao |
| collection | DOAJ |
| description | This paper is focused on studying approximate damped oscillatory solutions of the compound KdV-Burgers-type equation with nonlinear terms of any order. By the theory and method of planar dynamical systems, existence conditions and number of bounded traveling wave solutions including damped oscillatory solutions are obtained. Utilizing the undetermined coefficients method, the approximate solutions of damped oscillatory solutions traveling to the left are presented. Error estimates of these approximate solutions are given by the thought of homogeneous principle. The results indicate that errors between implicit exact damped oscillatory solutions and approximate damped oscillatory solutions are infinitesimal decreasing in the exponential form. |
| format | Article |
| id | doaj-art-2aa70a711d5f46d6b67f4eb60ab44d52 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2aa70a711d5f46d6b67f4eb60ab44d522025-02-03T05:44:00ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/935915935915A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary ResultsYan Zhao0Weiguo Zhang1College of Engineering, Peking University, Beijing 100871, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaThis paper is focused on studying approximate damped oscillatory solutions of the compound KdV-Burgers-type equation with nonlinear terms of any order. By the theory and method of planar dynamical systems, existence conditions and number of bounded traveling wave solutions including damped oscillatory solutions are obtained. Utilizing the undetermined coefficients method, the approximate solutions of damped oscillatory solutions traveling to the left are presented. Error estimates of these approximate solutions are given by the thought of homogeneous principle. The results indicate that errors between implicit exact damped oscillatory solutions and approximate damped oscillatory solutions are infinitesimal decreasing in the exponential form.http://dx.doi.org/10.1155/2014/935915 |
| spellingShingle | Yan Zhao Weiguo Zhang A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results Journal of Applied Mathematics |
| title | A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results |
| title_full | A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results |
| title_fullStr | A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results |
| title_full_unstemmed | A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results |
| title_short | A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results |
| title_sort | class of approximate damped oscillatory solutions to compound kdv burgers type equation with nonlinear terms of any order preliminary results |
| url | http://dx.doi.org/10.1155/2014/935915 |
| work_keys_str_mv | AT yanzhao aclassofapproximatedampedoscillatorysolutionstocompoundkdvburgerstypeequationwithnonlineartermsofanyorderpreliminaryresults AT weiguozhang aclassofapproximatedampedoscillatorysolutionstocompoundkdvburgerstypeequationwithnonlineartermsofanyorderpreliminaryresults AT yanzhao classofapproximatedampedoscillatorysolutionstocompoundkdvburgerstypeequationwithnonlineartermsofanyorderpreliminaryresults AT weiguozhang classofapproximatedampedoscillatorysolutionstocompoundkdvburgerstypeequationwithnonlineartermsofanyorderpreliminaryresults |