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In this paper, the accurate closed-form solutions of the Manakov-system are extracted via the extended-expansion method, the-expansion method and generalized Kudryashov method. The solutions are obtained in the form of trigonometric, hyperbolic and rational functions. The dynamical behaviour of obtained solutions is discussed by plotting 3D graphs, 2D contour graphs and density graphs. The symbolic softwares such as Maple and Mathematica are used to plot the graphs of retrieved solutions. The modulation instability (MI) of Manakov-system is also discussed in this paper.

Travelling wave solutions and modulation instability analysis of the nonlinear Manakov-system