Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1994-04-26
Nonlinear Sciences
Exactly Solvable and Integrable Systems
9 pages in plain TeX
Scientific paper
10.1016/0375-9601(94)90367-0
We introduce multilinear operators, that generalize Hirota's bilinear $D$ operator, based on the principle of gauge invariance of the $\tau$ 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.
Grammaticos Basil
Hietarinta Jarmo
Ramani Alfred
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