Abstract
One of the most powerful methods for finding and solving integrable nonlinear partial dierential equations is Hirota’s bilinear method. The idea behind it is to make first a nonlinear change in the dependent variables after which multisoliton solutions of integrable systems can be expressed as polynomials of exponentials e i where the 0s are linear in the independent variables. Among all quadratic expressions homogeneous in the derivatives, Hirota’s bilinear form can be isolated by a gauge symmetry: it is the only one that is invariant under f ! e f where is linear in the variables. This suggest a generalization to multilinear equations using the same gauge symmetry. The set of gauge invariant multilinear dierential equations can then be studied and
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