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Limit symmetry of the Korteweg-de Vries equation and its applications

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Abstract

We discuss a symmetry of the Korteweg-de Vries (KdV) equation. This symmetry can be related to the squared eigenfunction symmetry by a limit procedure. As applications, we consider the similarity reduction of the KdV equation and a KdV equation with new self-consistent sources. We derive some solutions via a bilinear approach.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, China

    Da-jun Zhang, Jian-bing Zhang & Qing Shen

  2. School of Mathematics Science, Xuzhou Normal University, Xuzhou, China

    Jian-bing Zhang

Authors
  1. Da-jun Zhang
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  2. Jian-bing Zhang
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  3. Qing Shen
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Corresponding author

Correspondence to Da-jun Zhang.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 163, No. 2, pp. 277–287, May, 2010.

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Zhang, Dj., Zhang, Jb. & Shen, Q. Limit symmetry of the Korteweg-de Vries equation and its applications. Theor Math Phys 163, 634–643 (2010). https://doi.org/10.1007/s11232-010-0046-y

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  • DOI: https://doi.org/10.1007/s11232-010-0046-y

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