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Hamiltonian theory for the DNLS equation with a squared spectral parameter

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Wuhan University Journal of Natural Sciences

Abstract

With a special gauge transformation, the Lax pair of the derivative nonlinear Shcrödinger (DNLS) equation turns to depend on the squared parameter λ = k 2 instead of the usual spectral parameter k. By introducing a new direct product of Jost solutions, the complete Hamiltonian theory of the DNLS equation is constructed on the basis of the squared spectral parameter, which shows that the integrability completeness is still preserved. This result will be beneficial to the further study of the DNLS equation, such as the direct perturbation method.

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Authors and Affiliations

  1. School of Physics and Technology, Wuhan University, Wuhan, 430072, Hubei, China

    Jin Zhang, Tian Yan & Hao Cai

Authors
  1. Jin Zhang
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  2. Tian Yan
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  3. Hao Cai
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Corresponding author

Correspondence to Hao Cai.

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Foundation item: Supported by the National Natural Science Foundation of China (10705022)

Biography: ZHANG Jin, female, Master candidate, research direction: nonlinear equation.

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Zhang, J., Yan, T. & Cai, H. Hamiltonian theory for the DNLS equation with a squared spectral parameter. Wuhan Univ. J. Nat. Sci. 15, 315–319 (2010). https://doi.org/10.1007/s11859-010-0658-y

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  • DOI: https://doi.org/10.1007/s11859-010-0658-y

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