Strong non-monotonic behavior of particle density of solitary waves of nonlinear Schrödinger equation in Bose–Einstein condensates

Global Non-monotonicity of Solutions to Nonlinear Second-Order Differential Equations

“…Although lack of monotonicity has received much less attention in the literature, a number of interesting results in this direction have been reported by Cecchi et al [3], Detki [5,6], Lepin [16,17] and other authors. It should be noted that non-monotone behavior is observed in many phenomena in applied sciences; see, for instance, the papers by Pašić [26] or Zhang [38] and the references cited therein. Complementing the aforementioned studies, in this paper we obtain sufficient conditions which ensure non-monotonicity of all extendable solutions to Eqs.…”