Multi-component decompositions, linear superpositions, and new nonlinear integrable coupled KdV-type systems

The existence of decompositions of the nonlinear integrable systems not only permits us to establish so-called linear superposition solutions but also to derive new nonlinear integrable coupled systems. Restricting our attention to the single component decompositions of the potential BKP hierarchy, we obtain that suitable linear superpositions of some decomposition solutions still satisfy the same equations. In parallel, successful attempts are made by multi-component decompositions of the potential BKP hierarchy to construct linear superposition solutions and new nonlinear integrable coupled KdV-type systems that a change of dependent variables cannot decouple.