Several well-known nonlinear waves in the rational solutions of the nonlinear Schrödinger equation are studied in two-component plasmas consisting of ions fluid and nonextensive electrons, such as Kuznetsov–Ma breather (K-M), bright soliton, rogue wave (RW), Akhmediev breather (AB) and dark soliton, and so on. In this paper, we have investigated the characteristics of K-M, AB, and RW's propagation in plasma with nonextensive electron distribution, and the dependence of amplitude and width for ion acoustic rogue waves in this system. It is found that K-M' triplet is appearance-disappearance-appearance-disappearance. AB solitons only appear once and RW is a single wave that appears from nowhere and then disappears. It is also noted that the wave number and nonextensive parameter of electrons have a significant influence on the maximum envelope amplitude, but, the influence of the width was not significant. At the same time, the effects of the small parameter, which represent the nonlinear strength, on the amplitude and width of ion acoustic rogue waves are also being highlighted.

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