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The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy

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Abstract

By using a general scheme for decomposing a zero-curvature equation into two commutingx- andt n -finite-dimensional integrable Hamiltonian systems (FDIHS), a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint representation of the two auxiliary linear problems is presented. The Darboux transformation for these FDIHSs is derived.

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Authors and Affiliations

  1. Department of Applied Mathematics, Tsinghua University, 100084, Beijing, China

    Zeng Yunbo

  2. Department of Mathematics, University of Science and Technology of China, 230026, Hefei, China

    Li Yishen

Authors
  1. Zeng Yunbo
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  2. Li Yishen
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Supported by the Chinese National Basic Research Project “Nonlinear Science”

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Yunbo, Z., Yishen, L. The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy. Acta Mathematica Sinica 12, 217–224 (1996). https://doi.org/10.1007/BF02108164

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  • DOI: https://doi.org/10.1007/BF02108164

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