Abstract
A method is presented for the construction of W shaped-W shaped solitons and W-shaped soliton combined with other types of solitons to coupled nonlinear partial differential equations (NLPDEs). This method is applied to investigate the propagation of new progressive solitons in magneto-optical waveguides that carry the quadratic-cubic nonlinearity described by a coupled system of nonlinear Schr\(\ddot{\textrm{o}}\)dinger equations. These waveguides have a great advantage since they control solitons’ clutter effects and thus assure their smooth propagation across intercontinental distances. Many approaches to investigating the exact solitons and other solutions to nonlinear models are often very powerful and very efficient to deal with single NLPDEs, however they do not always have the same success when applied to coupled NLPDEs. This difficulty is due to the existence of interaction terms in the coupled equations. For this reason, it is not always an easy task to derive exact solutions to these coupled equations. To overcome this difficulty, several authors have attempted to solve coupled equations by making the assumption that the solution in one line is proportional to the solution in another line, leading to an excessive imposition of constraints. This leads to the reduction of coupled equations to a single one. By doing so, they denature the physical phenomena described by the original coupled NLPDEs. We propose here a method that gives a better perspective in handling the analytical investigation of coupled NLPDEs. The novelty lies on the fact that it not only allows the propagation of different types of solutions in two lines to be conducted in just one move, but it also retrieves the propagation of same types of solutions in the two lines. For this latter case, the solutions come naturally with less constraints.The criteria for these solutions to exist are also exhibited in the form of parameter constraints.
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Yomba, E. Method of searching for a W-shaped like soliton combined with other families of solitons in coupled equations: application to magneto-optic waveguides with quadratic-cubic nonlinearity. Opt Quant Electron 56, 752 (2024). https://doi.org/10.1007/s11082-023-06218-1
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DOI: https://doi.org/10.1007/s11082-023-06218-1