Optik solitons to LPD model by some integration algorithms

This study first obtains the dark and singular optical soliton solutions of the Lakshmanan-Porsezian-Daniel equation for Kerr's law nonlinearity by using two integration schemes. These are Jacobi's extended elliptic function approximation and exp(-ϕ(η))-expansion method. Existence criteria, which are presented as constraint conditions for these solitons, have also been obtained. As a by-product, periodic singular solutions were obtained and these are also listed in the study. It then integrates the vector-linked Lakshmanan-Porsezian-Daniel equation in birefringent fibers with the help of the extended Jacobi elliptic function expansion scheme. Jacobi double periodic wave solutions were obtained. Solutions obtained by this integration mechanism lead to dark solitons or singular solitons or periodic solutions in the limiting case.