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.

AKNS Formalism and Exact Solutions of KdV and Modified KdV Equations with Variable-Coefficients

“…However, literature on nonlinear evolution equations with variable-coefficients [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39] is rather limited compared to the constant coefficient counterparts. The AKNS hierarchy of nonlinear evolution equations with variable-coefficients has not been much studied.…”

Painlevé property, Lax pair and Darboux transformation of the variable-coefficient modified Kortweg-de Vries model in fluid-filled elastic tubes

“…(1). Then with the Ablowitz-Kaup-Newell-Segur (AKNS) procedure [33,34] and symbolic computation [22][23][24][25][26][27][28][29]35], the Lax pair of Eq. (1) will be constructed.…”

The Bright Soliton Solutions of Two Variable-Coefficient Coupled Nonlinear Schr¨odinger Equations in Optical Fibers

“…In many branches of physics, considering the inhomogeneities of media and non-uniformities of bound-0932-0784 / 10 / 0100-0071 $ 06.00 c 2010 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com aries such as for a Bose gas of impenetrable bosons [6], optical fibre communications [7,8], variablecoefficient nonlinear wave equations can describe real situations more powerfully than their constant coefficient counterparts. Although such variable coefficients often make the studies hard, with the development of symbolic computation [8,9], it is becoming possible and exercisable for a computer to deal with them.…”

“…Although such variable coefficients often make the studies hard, with the development of symbolic computation [8,9], it is becoming possible and exercisable for a computer to deal with them.…”