Real-valued non-analytic solutions for the generalized Korteweg-de Vries equation
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- by A. Alexandrou Himonas and Gerson Petronilho PDF
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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.References
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Additional Information
- A. Alexandrou Himonas
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 86060
- Email: himonas.1@nd.edu
- Gerson Petronilho
- Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos - SP 13565-905, Brazil
- MR Author ID: 250320
- Email: gerson@dm.ufscar.br
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2801615