Spatiotemporal traveling and solitary wave solutions to the generalized nonlinear Schrödinger equation with single- and dual-power law nonlinearity

We generalize previously obtained solutions to the generalized nonlinear Schrödinger equation (NLSE) with cubic-quintic nonlinearity and distributed coefficients to obtain spatiotemporal traveling and solitary wave solutions for the NLSE with a general p-2p dual-power law nonlinearity, where p is an arbitrary positive real number (the cubic-quintic model being a special case for $p=2$). In addition, it is possible to eliminate the lower exponent, producing spatiotemporal traveling and solitary wave solutions to the NLSE with a single power law nonlinearity of arbitrary positive real power, which models many important systems including superfluid Fermi gas.