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 is not a multiple of four. In the case that , that is, the non-linearity is of the form , where 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.