📒 This book deals with the study of Modulational instability and solitary wave or soliton-like solutions for various structure of Nonlinear Schrödinger equation(NLSE). We have illustrated the properties of negative index materials (NIMs) and studied the solitary wave solutions for higher order NLSE, NLSE with source and NLSE in coupled mode. In this book we have investigated MI for twin-core fiber which is physical system of considerable interest. MI is responsible for soliton pulses in different nonlinear media. We have also illustrated the the solitary wave solutions for HNLSE for ordinary nonlinear materials and also discussed the impact of source term on MI in case of NLSE with source.