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Constructing analytical solutions for non-liner partial differential equations arising in thermal and fluid science is important and interesting. In this paper, Hirota’s bi-linear method is extended to a new generalized Ablowitz-Kaup-Newell-Segur hierarchy which includes heat conduction equation, advection equation, advection-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 solutions of the generalized Ablowitz-Kaup-Newell-Segur hierarchy are obtained

Analytical treatment on a new generalized Ablowitz-Kaup-Newell-Segur hierarchy of thermal and fluid equations