We derive the integrability conditions of nonautonomous nonlinear Schrödinger equations using the Lax pair and similarity transformation methods. We present a comparative analysis of these integrability conditions with those of the Painlevé method. We show that while the Painlevé integrability conditions restrict the dispersion, nonlinearity, and dissipation/gain coefficients to be space independent and the external potential to be only a quadratic function of position, the Lax Pair and the similarity transformation methods allow for space-dependent coefficients and an external potential that is not restricted to the quadratic form. The integrability conditions of the Painlevé method are retrieved as a special case of our general integrability conditions. We also derive the integrability conditions of nonautonomous nonlinear Schrödinger equations for two- and three-spacial dimensions.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics