Supersymmetric Open 2-branes And Nonlinear Schrdinger Equation

This thesis is divided into two parts, the ?rst part studies the quantization and spectrum of RNS supersymmetric open 2-brane. Starting from the Polyakov action, the classical equations of motion are obtained. The quantization scheme used is a hybrid of canonical and light-cone quantization. The model is studied in a ?at worldvolume metric, which physically corresponds to partly ?xing the dynamics of the supersymmetric open 2-brane to some ?xed points in the phase space.The Hamiltonian in terms of raising and lowering operators is obtained. The world-volume supersymmetry cancels the normal ordering constant in the Rsector. In order to realize spacetime supersymmetry in the model, a speci?c value for the zeta function regularization of an in?nite sum is conjectured in the NS sector. Some more new states are obtained in both the NS-Sector and R-Sector spectrum of states. The NS-Sector spectrum contains tachyons, and to remove these tachyons we resort to a GSO-like condition. The truncated spectrum is discrete and is shown to assure that spacetime supersymmetry is realized atleast at the massless and ?rst massive level in the spectrum of states of the supersymmetric open 2-brane.The second part deals with the study of the behavior of a discrete nonlinear Schr¨odinger dimer and the stability of its solutions by adding more than one nonlinear couplings or the nonlocal nonlinearities. We study the e?ects of these new terms theoretically and compare the results with previously known result. We will only consider the classical model in this thesis.