Solutions of the nonlinear Schnödinger's equation with resonant nonlinearity

In this thesis, firstly, the resonant nonlinear Schrödinger equation was investigated using the extended Jacobi function expansion method with two different forms of nonlinearity. The dark and singular soliton solutions of this equation were obtained. Later, the resonant nonlinear Schrödinger equation was examined with four different forms of nonlinearity. This equation was also considered with time-dependent coefficients. The simplest equation method was applied to solve the addressed equations, and then exact 1-soliton solutions were obtained. It can be said that this method is a powerful mathematical technique for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics. The soliton solutions of the resonant nonlinear Schrödinger equation in optical fibers with time-dependent coefficients were examined using the simplest equation approach.