Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

This paper retrieves some new optical solutions to the Kundu–Mukherjee–Naskar (KMN) equation in the context of nonlinear optical fiber communication systems. In this regard, a complex transformation is applied to the integer-order KMN equation for converting it to an ordinary differential equation (ODE). Then, the generalized Kudryashov method (gKM) and the new auxiliary equation method (NAEM) are employed to the ODE. As consequence, dark, bright, periodic U -shaped, and singular soliton solutions are explored to the ODE. The discrepancies between the results obtained in the present study and the previously obtained solutions through different methods are discussed. Furthermore, the time-fractional derivative and an oblique wave transformation in conjunction with the mentioned methods are executed to the fractional-order KMN equation. All obtained wave solutions are found to be new in terms of fractionality, wave obliqueness, and applied methods sense. The effects of obliqueness and fractionality on the attained solutions are demonstrated graphically along with its physical descriptions. It is found that the optical wave phenomena are changed with the increase of obliqueness as well as fractionality. It is also found that both the applied methods are suitable for acquiring new optical soliton features to the KMN equation with or without fractional and obliqueness conditions. However, the NAEM is capable of exploring more solutions of the considered equation over the gKM. Precisely, it can be assured that the utilized methods and the relevant transformation are powerful over the other methods. Therefore, the methods can be applied for further studies to explain the various physical phenomena arising in optical fiber communication systems.

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