Breather structures in a plasma with warm ions and Cairns electrons

The modulational instability (MI) of ion‐acoustic waves (IAWs) in a two‐component non‐Maxwellian hot plasma with Cairns distributed electrons is investigated. Using the derivative expansion method, a non‐linear Schrödinger equation (NLSE) is obtained. The criterion for MI, which occurs for small values of the carrier wavenumber, is obtained. It is found that non‐thermal parameter α modifies the criteria for MI instability. The analytical solutions of NLSE in the form of various types of freak waves, including the Peregrine soliton, the Akhmediev breather, and the Kuznetsov–Ma breather, are examined. The effects of the non‐thermal parameter as well as ion‐to‐electron temperature ratio on the rogue wave profile are discussed. Our results should be relevant to wave propagation stability. Non‐thermal models may play an increasingly important role in predicting complex plasma behaviour and understanding the underlying physical processes.