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Soliton equations related to the affine Kac-Moody algebra D (1)4

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Abstract

We have derived the hierarchy of soliton equations associated with the untwisted affine Kac-Moody algebra D (1)4 by calculating the corresponding recursion operators. The Hamiltonian formulation of the equations from the hierarchy is also considered. As an example we have explicitly presented the first non-trivial member of the hierarchy, which is an one-parameter family of mKdV equations. We have also considered the spectral properties of the Lax operator and introduced a minimal set of scattering data.

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Authors and Affiliations

  1. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784, Sofia, Bulgaria

    V. S. Gerdjikov

  2. Theoretical Physics Department, Faculty of Physics, Sofia University “St. Kliment Ohridski”, 5 James Bourchier Blvd, 1164, Sofia, Bulgaria

    D. M. Mladenov, A. A. Stefanov & S. K. Varbev

  3. Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784, Sofia, Bulgaria

    S. K. Varbev

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  1. V. S. Gerdjikov
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  4. S. K. Varbev
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Gerdjikov, V.S., Mladenov, D.M., Stefanov, A.A. et al. Soliton equations related to the affine Kac-Moody algebra D (1)4 . Eur. Phys. J. Plus 130, 106 (2015). https://doi.org/10.1140/epjp/i2015-15106-5

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