In this thesis, we investigate exact analytical solutions of nonlinear Schrodinger type equations which govern the propagation of soliton pulses through optical fi bres. The equations under consideration are generalised nonlinear Schrodinger equation of third order, perturbed Gerdjikov-Ivanov equation and the Lakshmana Porsezian-Daniel model equation. The methods employed for the solution are auxiliary equation method, improved projective Riccati equation method and Bernoulli sub-ODE method. We have derived a variety of solutions in terms of Jacobi elliptic functions (JEFs) and their infinite period counterparts when the modulus of the JEFs approaches 1. The solutions obtained are dark, bright, sin gular, W-shaped solitons, etc. The constraint conditions for the solutions to exist have also been found. The physical interpretations of the obtained results are represented by depicting the plots of some selected solutions. The modulation instabilities of the GI equation and the LPD model have also been investigated.