Solitary waves of equation for propagation pulse with power nonlinearities

The equation for propagation pulse with power nonlinearities is studied. The first integrals of equations corresponding to the real and imaginary parts are presented. By means of the first integrals the nonlinear first-order differential equation is given. Using the simplest equations method we look for the solitary wave solutions. Three forms of the solitary wave solutions of the equation are found.