Some integrable hierarchies in (2+1) dimensions and their twistor description
- 1 January 1993
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 34 (1) , 243-259
- https://doi.org/10.1063/1.530379
Abstract
The twistor space construction, due to Mason and Sparling, for solutions of the nonlinear Schrödinger and Korteweg–deVries hierarchies is generalized, resulting in families of integrable models in (2+1) dimensions. Soliton solutions to one such hierarchy [associated with the gauge group SU(2)] are constructed by adapting the methods used to construct instanton and monopole solutions. These integrable models have the feature that their solutions depend on a number of arbitrary functions as well as arbitrary constants, in contrast to the closely related Davey–Stewartson hierachy.Keywords
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