Self-similar solutions for some nonlinear evolution equations : KdV, mKdV and burgers equations
Joint Authors
al-Wakil, S. A.
Abu al-Wafa, Isam M.
al-Hanbali, A. M.
al-Shewi, E. K.
Abd al-Hamid, H. M.
Source
Arab Journal of Basic and Applied Sciences
Issue
Vol. 19, Issue 0 (29 Feb. 2016), pp.44-51, 8 p.
Publisher
University of Bahrain College of Science
Publication Date
2016-02-29
Country of Publication
Bahrain
No. of Pages
8
Main Subjects
Topics
Abstract EN
A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented.
The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed.
The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions.
These solutions appear as new types of solitary, shock and periodic waves.
Also, the method can be applied to other nonlinear evolution equations in mathematical physics.
American Psychological Association (APA)
al-Wakil, S. A.& Abu al-Wafa, Isam M.& al-Hanbali, A. M.& al-Shewi, E. K.& Abd al-Hamid, H. M.. 2016. Self-similar solutions for some nonlinear evolution equations : KdV, mKdV and burgers equations. Arab Journal of Basic and Applied Sciences،Vol. 19, no. 0, pp.44-51.
https://search.emarefa.net/detail/BIM-668491
Modern Language Association (MLA)
al-Wakil, S. A.…[et al.]. Self-similar solutions for some nonlinear evolution equations : KdV, mKdV and burgers equations. Arab Journal of Basic and Applied Sciences Vol. 19 (Feb. 2016), pp.44-51.
https://search.emarefa.net/detail/BIM-668491
American Medical Association (AMA)
al-Wakil, S. A.& Abu al-Wafa, Isam M.& al-Hanbali, A. M.& al-Shewi, E. K.& Abd al-Hamid, H. M.. Self-similar solutions for some nonlinear evolution equations : KdV, mKdV and burgers equations. Arab Journal of Basic and Applied Sciences. 2016. Vol. 19, no. 0, pp.44-51.
https://search.emarefa.net/detail/BIM-668491
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 50-51
Record ID
BIM-668491