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Proceedings of the American Mathematical Society

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Real-valued non-analytic solutions for the generalized Korteweg-de Vries equation


Authors: A. Alexandrou Himonas and Gerson Petronilho
Journal: Proc. Amer. Math. Soc. 139 (2011), 2759-2766
MSC (2010): Primary 35Q53; Secondary 37K10
DOI: https://doi.org/10.1090/S0002-9939-2011-10983-3
Published electronically: February 22, 2011
MathSciNet review: 2801615
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Abstract: In both the periodic and non-periodic cases, non-analytic in time solutions to the Cauchy problem of the gKdV equation are constructed with real-valued analytic initial data when $ k$ is not a multiple of four. In the case that $ k=4\ell$, that is, the non-linearity is of the form $ u^{4\ell}\partial_xu$, where $ \ell$ is a positive integer, then non-analytic in time solutions are available only for complex-valued initial data.


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Additional Information

A. Alexandrou Himonas
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: himonas.1@nd.edu

Gerson Petronilho
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos - SP 13565-905, Brazil
Email: gerson@dm.ufscar.br

DOI: https://doi.org/10.1090/S0002-9939-2011-10983-3
Keywords: Generalized Korteweg-de Vries equation, gKdV, Cauchy problem, periodic, non-periodic, analytic solutions
Received by editor(s): July 16, 2010
Published electronically: February 22, 2011
Additional Notes: The second author was partially supported by CNPq and Fapesp
Communicated by: Walter Craig
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.