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ANALYTICAL TREATMENT ON A NEW GENERALIZED ABLOWITZ-KAUP-NEWELL-SEGUR HIERARCHY OF THERMAL AND FLUID EQUATIONS

ABSTRACT
Constructing analytical solutions for non-liner partial differential equations aris-ing in thermal and fluid science is important and interesting. In this paper, Hiro-ta's bi-linear method is extended to a new generalized Ablowitz-Kaup-Newell-Se-gur hierarchy which includes heat conduction equation, advection equation, ad-vection-dispersion equation, and Korteweg-de Vries equation as special cases. As a result, bi-linear form of the generalized Ablowitz-Kaup-Newell-Segur hierarchy is derived. Based on the derived bi-linear form, exact and explicit n-soliton solu-tions of the generalized Ablowitz-Kaup-Newell-Segur hierarchy are obtained.
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PAPER SUBMITTED: 2016-06-23
PAPER REVISED: 2016-10-15
PAPER ACCEPTED: 2016-10-25
PUBLISHED ONLINE: 2017-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI160623042Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE 4, PAGES [1607 - 1612]
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© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence