Abstract
We discuss the Camassa-Holm equation perturbed in Schwartz class around a suitable constant. This paper is concerned with the wave breaking mechanism for periodic case where two special classes of initial data were involved. The asymptotic behavior of solutions is also analyzed in the following sense: the corresponding solution to initial data with algebraic decay at infinity will retain this property at infinity in its lifespan.
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Zhu, X. On a Shallow Water Equation Perturbed in Schwartz Class. Math Phys Anal Geom 15, 317–329 (2012). https://doi.org/10.1007/s11040-012-9112-z
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DOI: https://doi.org/10.1007/s11040-012-9112-z