Bäklund transformations and singular integral equations

G.R.W. Quispel, F.W. Nijhoff, H.W. Capel and J.van der Linden

Physica A: Statistical Mechanics and its Applications, 1984, vol. 123, issue 2, 319-359

Abstract: A systematic method for deriving Bäcklund transformations for singular (linear) integral equations is presented. The method leads in a natural way to the Bäcklund transformations for the corresponding (integrable) nonlinear partial differential equations. By repeated use of the method a hierarchy of singular integral equations and Bäcklund transformations can be derived, corresponding to so-called multi-modified partial differential equations. Specific examples include the Korteweg-de Vries equation and the first, second, and third modified Korteweg-de Vries equation; the Nonlinear Schrödinger equation and the Anisotropic Heisenberg Spin Chain; the sine-Gordon equation and the modified sine-Gordon equation.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:123:y:1984:i:2:p:319-359

DOI: 10.1016/0378-4371(84)90159-6

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