| Summary: | Abstract This paper explores the head-on collision between two-counter propagating positron acoustic solitons and double layers (DLs) in an unmagnetized collisionless plasma having mobile cold positrons fluid, immobile positive ions and ( $$r,\;q$$ r , q )-distributed hot positrons, and hot electrons. By employing the extended Poincaré–Lighthill–Kuo method, the coupled Korteweg–de Vries (KdV), modified KdV (mKdV) and Gardner equations are derived to archive this goal. The effect of dimensionless parameters on the propagation characteristics of interacting KdV solitons (KdVSs), mKdV solitons (mKdVSs), Gardner solitons (GSs) and DLs are examined in detail by considering the limiting cases of ( $$r,\;q$$ r , q )-distribution. It is noted that the interaction of GSs and DLs are reported for the first time. The outcomes might be comprehended and beneficial not only in space and astrophysical environments but also in laboratory studies.
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