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The existence of decompositions of the nonlinear integrable systems not onlypermits us to establish so-called linear superposition solutions but also toderive new nonlinear integrable coupled systems. Restricting our attention tothe single component decompositions of the potential BKP hierarchy, we obtainthat suitable linear superpositions of some decomposition solutions stillsatisfy the same equations. In parallel, successful attempts are made bymulti-component decompositions of the potential BKP hierarchy to constructlinear superposition solutions and new nonlinear integrable coupled KdV-typesystems that a change of dependent variables cannot decouple.

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