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Abstract
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This paper considers the coupled Fokas–Lenells equation, which is used to study the transmission of signals through a polarization-preserving optical fibre. Its several solutions can play
an insignificant role in describing the soliton dynamics of optical fibres. Two techniques, the
Sine-Gordon expansion method and the rapidly convergent approximation methods, are applied
in this context to hunt down its exact solutions. It is established that all solutions derived
by the Sine-Gordon expansion method are particular cases of two-exponential solution sets
obtained by the rapidly convergent approximation method. Derived solutions are recast in a
variety of bright and dark solutions, as well as periodic solutions. A few important solutions
among them are plotted and analysed to get an idea about the transmission of signals through
a polarization-preserving optical fibre.
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