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On Decay Properties of Solutions of the k-Generalized KdV Equation

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Abstract

We prove special decay properties of solutions to the initial value problem associated to the k-generalized Korteweg-de Vries equation. These are related with persistence properties of the solution flow in weighted Sobolev spaces and with sharp unique continuation properties of solutions to this equation. As an application of our method we also obtain results concerning the decay behavior of perturbations of the traveling wave solutions as well as results for solutions corresponding to special data.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Nacional de Colombia, A. A. 3840, Medellin, Colombia

    Pedro Isaza

  2. IMPA, Instituto Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil

    Felipe Linares

  3. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    Gustavo Ponce

Authors
  1. Pedro Isaza
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  2. Felipe Linares
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  3. Gustavo Ponce
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Correspondence to Felipe Linares.

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Communicated by W. Schlag

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Isaza, P., Linares, F. & Ponce, G. On Decay Properties of Solutions of the k-Generalized KdV Equation. Commun. Math. Phys. 324, 129–146 (2013). https://doi.org/10.1007/s00220-013-1798-7

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  • DOI: https://doi.org/10.1007/s00220-013-1798-7

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