## THERMAL SCIENCE

International Scientific Journal

### 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.

**KEYWORDS**

PAPER SUBMITTED: 2016-06-23

PAPER REVISED: 2016-10-15

PAPER ACCEPTED: 2016-10-25

PUBLISHED ONLINE: 2017-09-09

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**4**, PAGES [1607 - 1612]

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