Conservation laws and dark-soliton solutions of an integrable higher-order nonlinear Schrödinger equation for a density-modulated quantum condensate. (25th March 2015) - Liu, De-Yin; Tian, Bo; Sun, Wen-Rong; Wang, Yun-Po
Abstract: In this paper, an integrable higher-order nonlinear Schrödinger equation for a density-modulated quantum condensate is investigated. Based on the Ablowitz–Kaup–Newell–Segur system, an infinite number of conservation laws are obtained. Introducing an auxiliary function, we derive the bilinear forms and construct the dark-soliton solutions with the help of the Hirota method and symbolic computation. Dark one, two, and three solitons are analyzed graphically. Via asymptotic analysis, interactions between the two dark solitons are proved to be elastic. We see that the coefficients in the equation only affect the soliton velocity. We analyze the linear stability of the plane wave solutions in the presence of a small perturbation.