Optical solitons with spatio-temporal dispersion by first integral approach and functional variable method

This paper applies the first integral method and functional variable technique in order to obtain optical solitons from the governing nonlinear Schrödinger's equation with spatio-temporal dispersion. There are four types of nonlinear media that are taken into account. These are Kerr law, power law, parabolic law as well as the dual-power law nonlinearity. Several constraint conditions naturally emerge from the results obtained and these conditions are also listed.