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A very important nonlinear equation in science is the Nonlinear Schrodinger equation (NLS) i + (1) at This is a partial differential equation. Devise a numerical scheme to solve this equation. Apply periodic boundary conditions for all time: (0, t) = 1(L, t) (2) L is the length of the integration domain. From the literature you can find an analytic solution to Eq. (1) that is called a soliton. It will have a form like exp(..)sech(...) with 2 free parameters. These parameters control the soliton speed and amplitude. Problem (a) Device a numerical scheme that will successfully follow the evolution of the exact 1-soliton solution of Eq. (1). Follow this soliton as it performs at least 3 transits of the spatial region [0, L]. The soliton should travel without any distortion. Plot the time evolution of your numerical solution