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

B. Grammaticos; A. Ramani; J. Hietarinta

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

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arXiv · solv-int/9404006

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

B. Grammaticos·A. Ramani·J. Hietarinta

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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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B. Grammaticos, A. Ramani, J. Hietarinta. 1994-04-26. Multilinear Operators: The Natural Extension Of Hirota's Bilinear Formalism. https://doi.org/10.1016/0375-9601(94)90367-0

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