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Global conservative solutions of the Camassa-Holm equation. (English) Zbl 1105.76013
Summary: This paper develops a new approach to the analysis of Camassa-Holm equation. By introducing a new set of independent and dependent variables, the equation is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation. These new variables resolve all singularities due to possible wave breaking. Returning to the original variables, we obtain a semigroup of global solutions, depending continuously on initial data. Our solutions are conservative, in the sense that the total energy equals a constant, for almost every time.
MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25Solitary waves (inviscid fluids)
35Q35PDEs in connection with fluid mechanics
35Q51Soliton-like equations
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