Abstract
Soliton solutions which signify long wave parallel to the magnetic fields of Kaup–Newell optical fiber model are discussed in this paper by two different methods. The improved simple equation method (ISEM) and exp[Formula: see text]-expansion scheme are employed to solve the model to construct the solutions of the model in different cases. The achieved solutions are represented in different and general forms such as logarithmic or exponential function, trigonometric and hyperbolic trigonometric functions, etc. Also, the modulation instability of the model is analyzed which confirms that all obtained exact results are stable. Several solutions from achieved solutions are novel.
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