We present a Bäcklund transformation operating on solutions of the Kortweg-de Vries equation. It provides a unifying approach to the theory of solitary waves (solutions). Recursive application of the transformation to any solution of the Korteweg-de Vries equation generates a hierarchy of solutions for which an algebraic recursion relation is obtained. Every such hierarchy (one of which is the known family of pure multisoliton solutions) thus admits a nonlinear superposition principle.

• Received 2 August 1973

DOI:https://doi.org/10.1103/PhysRevLett.31.1386