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Wave‐breaking phenomenon for a generalized spatially periodic Camassa–Holm system
Author(s) -
Yu Shengqi
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3155
Subject(s) - gravitational singularity , mathematics , conservation law , camassa–holm equation , mathematical analysis , breaking wave , phenomenon , calculus (dental) , physics , wave propagation , integrable system , medicine , dentistry , quantum mechanics
Considered herein is a generalized two‐component Camassa–Holm system in spatially periodic setting. We first prove two conservation laws; then under proper assumptions on the initial data, we show the precise blow‐up scenarios and sufficient conditions guaranteeing the formation of singularities to the solutions of the generalized Camassa–Holm system. Copyright © 2014 John Wiley & Sons, Ltd.