On the Integrability Properties of a Perturbed Nonlinear Schrödinger Field Equation

The integrability properties of a perturbed nonlinear Schrödinger equation are studied using Painleve analysis and Laxs method. We distinguish between integrability in the Painleve sense and integrability in the Lax sense. The solution of the perturbed equation, with the perturbing term depending only on time, is found by direct integration. It is seen that the perturbing nonlinear inhomogeneity can split the fundamental soliton into pulses at high values of the perturbation strength.