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Multilinear Operators: The Natural Extension Of Hirota's Bilinear Formalism

1994/04/26 by B. Grammaticos, A. Ramani, J. Hietarinta
Physics and Astronomy · #nlin.SI #solv-int

paper · pdf · doi:10.1016/0375-9601(94)90367-0

9 pages in plain TeX

arxiv created 1994/04/26 · arxiv updated 2009/11/30

Abstract

We introduce multilinear operators, that generalize Hirota's bilinear D operator, based on the principle of gauge invariance of the τ functions. We show that these operators can be constructed systematically using the bilinear D's as building blocks. We concentrate in particular on the trilinear case and study the possible integrability of equations with one dependent variable. The 5th order equation of the Lax-hierarchy as well as Satsuma's lowest-order gauge invariant equation are shown to have simple trilinear expressions. The formalism can be extended to an arbitrary degree of multilinearity.

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