Painleve Integrability of Nonlinear Schroedinger Equations with both Space- and Time-Dependent Coefficients

We investigate the Painleve integrability of nonautonomous nonlinear Schroedinger (NLS) equations with both space- and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)