Bistable solitons and the Painlevé test

In a previous publication [R. H. Enns, S. S. Rangnekar, and A. E. Kaplan, Phys. Rev. A 36, 1270 (1987)], it was demonstrated numerically that the generalized nonlinear Schrödinger equation (GNLSE) describing one-dimensional optical pulse propagation displays nondestructive collisions between bistable solitonlike pulses for a variety of nonlinear models including the model f(I=‖${\mathit{E}}^2$‖)+μ(I/${\mathit{I}}_0$)+(I/${\mathit{I}}_0$${)}^{\mathit{n}}$/[1+(I/${\mathit{I}}_0$${)}^{\mathit{n}}$] for n≥3. Here I is the intensity, E the complex electric field amplitude, μ and $I_0$ are real positive constants, and n takes on positive integer values. In this paper, we report that the GNLSE passes the analytical Painlevé test for the above model. Explicit formulas for the first few coefficients in the Painlevé expansion, as well as the compatibility conditions, are given for n≥3. Thus there exists at least one physically reasonable form of the GNLSE for which bistable solitons exist.