This paper studies the (1+1)-dimensional Kuramoto–Sivashinsky equation (1D-KSE) also known as canonical evolution equation within the context of flame front propagation, plasma instabilities, and phase turbulence in reaction–diffusion systems. We use Hirota’s derivatives to formulate bilinear equations and subsequently compute various types of solitons. We obtain lump solution, lump one strip, lump two strip, X-type, lump periodic solution, generalized breather and rogue wave solutions for our governing model with the help of Hirota bilinear method (HBM) and the ansatz approach. Breathers solutions may be used to improve the efficiency of fiber optic communication systems and solitons in plasma waves. Rogue wave solutions may be used for the safety of oil platforms and ships while lump wave solutions can be utilized in manipulating and controlling laser beams for materials processing or laser surgery. We also discuss one, two and other soliton interactions for 1D-KSE under some constraint conditions. These interactions may be discussed in plasma stability and confinement, which can control fusion as a future energy source.