Symbolic computation on integrable properties of a variable-coefficient Korteweg–de Vries equation from arterial mechanics and Bose–Einstein condensates

Abstract

Applicable in arterial mechanics, Bose gases of impenetrable bosons and Bose–Einstein condensates, a variable-coefficient Korteweg–de Vries (vcKdV) equation is investigated in this paper with symbolic computation. Based on the Ablowitz–Kaup–Newell–Segur system, the Lax pair and auto-Bäcklund transformation are constructed. Furthermore, the nonlinear superposition formula and an infinite number of conservation laws for the vcKdV equation are also derived. Special attention is paid to the analytic one- and two-solitonic solutions with their physical properties and possible applications discussed.