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Global well-posedness for a coupled modified KdV system

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Abstract

We prove the sharp global well-posedness result for the initial value problem (IVP) associated to the system of the modified Korteweg-de Vries (mKdV) equation. For the single mKdV equation such result has been obtained by using Mirura’s Transform that takes the KdV equation to the mKdV equation [8]. We do not know the existence of Miura’s Transform that takes a KdV system to the system we are considering. To overcome this difficulty we developed a new proof of the sharp global well-posedness result for the single mKdV equation without using Miura’s Transform. We could successfully apply this technique in the case of the mKdV system to obtain the desired result.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro — UFRJ, Ilha do Fundão, 21945-970, Rio de Janeiro, RJ, Brazil

    Adán J. Corcho

  2. Centro de Matemática, Universidade do Minho, 4710-057, Braga, Portugal

    Mahendra Panthee

Authors
  1. Adán J. Corcho
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  2. Mahendra Panthee
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Correspondence to Adán J. Corcho.

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Corcho, A.J., Panthee, M. Global well-posedness for a coupled modified KdV system. Bull Braz Math Soc, New Series 43, 27–57 (2012). https://doi.org/10.1007/s00574-012-0004-4

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  • DOI: https://doi.org/10.1007/s00574-012-0004-4

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