dorsal/arxiv
View SchemaMultilinear Operators: The Natural Extension Of Hirota's Bilinear Formalism
| Authors | B. Grammaticos, A. Ramani, J. Hietarinta |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9404006 |
| URL | https://arxiv.org/abs/solv-int/9404006 |
| DOI | 10.1016/0375-9601(94)90367-0 |
Abstract
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.
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"abstract": "We introduce multilinear operators, that generalize Hirota\u0027s bilinear $D$\noperator, based on the principle of gauge invariance of the $\\tau$ functions.\nWe show that these operators can be constructed systematically using the\nbilinear $D$\u0027s as building blocks. We concentrate in particular on the\ntrilinear case and study the possible integrability of equations with one\ndependent variable. The 5th order equation of the Lax-hierarchy as well as\nSatsuma\u0027s lowest-order gauge invariant equation are shown to have simple\ntrilinear expressions. The formalism can be extended to an arbitrary degree of\nmultilinearity.",
"arxiv_id": "solv-int/9404006",
"authors": [
"B. Grammaticos",
"A. Ramani",
"J. Hietarinta"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/0375-9601(94)90367-0",
"title": "Multilinear Operators: The Natural Extension Of Hirota\u0027s Bilinear Formalism",
"url": "https://arxiv.org/abs/solv-int/9404006"
},
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