Abstract
This paper studies the integrable Kuralay equation which is a kind of integrable spin system in (1＋1) dimensions. Several new exact solutions of different kinds such as optical solitons, solitary waves and elliptic function solutions of this equation are retrieved by utilizing two effective techniques, namely, the modified F-expansion method and the new extended auxiliary equation method. The modulation instability (MI) analysis of the model is studied by using the linear-stability analysis and the MI gain spectrum is acquired. Moreover, the multiplier approach is applied to retrieve the conservation laws. At last, physical interpretations of the obtained results are demonstrated.
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