Lump and Interaction Solution for the Nonlinear Schrödinger Equation

Abstract

Solitons are the special types of solitary waves which do not vary their shape and frequency during propagation speed and is also an attractive area of current research in nonlinear physics and mathematics as well as in fiber optics and communication technologies. There are many forms of solitons such as singular soliton, bright soliton, dark soliton and lump soliton. In this thesis, we acquire lumpsolitonsolutionsfor paraxial nonlinear Schr¨odinger equation (NLSE) with the aid of Hirota bilinear method (HBM). In space, lump soliton solutions are rationally positioned in every direction. We also get optical dromions for paraxial NLSE by using modified extended Tanh method. We get domain walls, singular dromions and combined dark-singular dromions. We also list the constraint conditions