Gauge symmetry and the generalization of Hirota's bilinear method

DOI

10.2991/jnmp.1996.3.3-4.2How to use a DOI?

Abstract

One of the most powerful methods for finding and solving integrable nonlinear partial differential 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 ei where the is 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 differential equations can then be studied and integrable equations identified e.g. by the Painlevé method. Some interesting new equations have been found in this way.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Jarmo Hietarinta
PY  - 1996
DA  - 1996/09/02
TI  - Gauge symmetry and the generalization of Hirota's bilinear method
JO  - Journal of Nonlinear Mathematical Physics
SP  - 260
EP  - 265
VL  - 3
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.3-4.2
DO  - 10.2991/jnmp.1996.3.3-4.2
ID  - Hietarinta1996
ER  -