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Constraints of the KP hierarchy and multilinear forms

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Abstract

We consider the trilinear form of the Kaup-Broer system which gives rise to solutions in Wronskian form. The Kaup-Broer system is connected with AKNS system through a gauge transformation. The AKNS hierarchy can be understood as a generalized 1-constraint of the KP hierarchy. Imposing that constraint on Sato's equation we obtain the basic trilinear form and moreover a hierarchy of trilinear equations governing the AKNS flows. Similary, hierarchies of multilinear forms are derived in the case of generalized k-constraints.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, 230026, Hefei. Anhui, People's Republic of China

    Yi Cheng & Bin Zhang

  2. Faehbereich 17-Mathematik/Informatik, Universität-GH Kassel, Holländische Str. 36, D-34109, Kassel, Germany

    Walter Strampp

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  1. Yi Cheng
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  2. Walter Strampp
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  3. Bin Zhang
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Communicated by M. Jimbo

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Cheng, Y., Strampp, W. & Zhang, B. Constraints of the KP hierarchy and multilinear forms. Commun.Math. Phys. 168, 117–135 (1995). https://doi.org/10.1007/BF02099585

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  • DOI: https://doi.org/10.1007/BF02099585

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