Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations

El-Wakil, S.A.; Abulwafa, Essam M.; El-hanbaly, A.M.; El-Shewy, E.K.; Abd-El-Hamid, H.M.

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dc.contributor.author	El-Wakil, S.A.
dc.contributor.author	Abulwafa, Essam M.
dc.contributor.author	El-hanbaly, A.M.
dc.contributor.author	El-Shewy, E.K.
dc.contributor.author	Abd-El-Hamid, H.M.
dc.date.accessioned	2018-07-29T10:32:13Z
dc.date.available	2018-07-29T10:32:13Z
dc.date.issued	2016
dc.identifier.issn	1815-3852
dc.identifier.uri	https://journal.uob.edu.bh:443/handle/123456789/1109
dc.description.abstract	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.	en_US
dc.language.iso	en	en_US
dc.publisher	University of Bahrain	en_US
dc.rights	Attribution-NonCommercial-ShareAlike 4.0 International	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-sa/4.0/	*
dc.subject	Self-similar solution
dc.subject	Symbolic computations
dc.subject	Exact solutions
dc.subject	KdV, mKdV and Burgers equations
dc.title	Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations	en_US
dc.type	Article	en_US
dc.source.title	Arab Journal of Basic and Applied Sciences
dc.abbreviatedsourcetitle	AJBAS