Optical soliton solutions and conservation laws of some nonlinear partial differential equations by the method of undetermined coefficients

Optical solitons are the most fundamental fabric that governs the telecommunications industry. These soliton molecules are responsible for intercontinental fiber-optic communications. In this study, optical soliton solutions and conservation laws of some nonlinear partial differential equations are investigated. Firstly, optical soliton solutions to the recently proposed Kudryashov's equation are obtained. Bright, dark and singular soliton solutions to the model under consideration are extracted by the help of the method of undetermined coefficients. The conservation laws are also listed that are written in terms of Gauss' hypergeometric functions. Several parameter restrictions, that naturally emerged during the derivation process, are also enumerated. Subsequently, bright, dark and singular soliton solutions with parabolic-nonlocal combo nonlinearity in polarization-preserving optical fibers are derived by the method of undetermined coefficients. The included perturbation terms are all of Hamiltonian type. Finally, cubic-quartic soliton solutions to the Lakshmanan-Porsezian-Daniel model by employing the method of undetermined coefficients are revealed. Both polarization-preserving fibers and birefringent fibers are studied. The conservation laws for polarization-preserving fibers are also recovered and enumerated. The existence criteria for the discovered solitons are also presented.