Bäcklund Transformation for Solutions of the Korteweg-de Vries Equation
- 3 December 1973
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 31 (23) , 1386-1390
- https://doi.org/10.1103/physrevlett.31.1386
Abstract
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.Keywords
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