Additional symmetries for integrable equations and conformal algebra representation |
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Authors: | A Yu Orlov E I Schulman |
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Institution: | (1) Institute for Automation and Electrometry of the Siberian Branch of the Academy of Sciences of the U.S.S.R., Novosibirsk, U.S.S.R.;(2) Present address: P. P. Shirshov Institute of Oceanology, 117218, Krasikova 23, Moscow, U.S.S.R.;(3) Institute for Water Problems of the Academy of Sciences of the U.S.S.R., Moscow, U.S.S.R. |
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Abstract: | We present a regular procedure for constructing an infinite set of additional (spacetime variables explicitly dependent) symmetries of integrable nonlinear evolution equations (INEEs). In our method, additional symmetry equations arise together with their L-A pairs, so that they are integrable themselves. This procedure is based on a modified dressing method. For INEEs in 1+1 dimensions, some appropriate symmetry equations are shown to form the vector fields on a circle S
1 algebra representation. In contrast to the so-called isospectral deformations, these symmetries result from conformal transformations of the associated linear problem spectrum. For INEEs in 2+1 dimensions, the commutation relations for symmetry equations are shown to coincide with operators
, with integer m, p. Some additional results about Kac-Moody algebra applications are presented. |
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Keywords: | |
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