Abstract
The principal realization of the basic representation of an affine Kac-Moody algebra can be applied to construct soliton solutions of hierarchies of partial differential equations, among them the KdV- and KP-equations.
In this construction, called orbit-construction, the equations of the hierarchy itself arise in Hirota bilinear form. Using the Goddard-Kent-Olive coset-construction of conformai field theory, we show that the equations are generated by a pair of commuting c=1/2 Virasoro algebras in the KdV-case. We end with a brief discussion of other cases.
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© 1990 Springer Science+Business Media New York
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Bais, F.A., de Vos, K. (1990). A Coset-Construction for Integrable Hierarchies. In: Chau, LL., Nahm, W. (eds) Differential Geometric Methods in Theoretical Physics. NATO ASI Series, vol 245. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-9148-7_29
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DOI: https://doi.org/10.1007/978-1-4684-9148-7_29
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-9150-0
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