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Consideration in this paper is the effect of varying fractional dissipation with the dissipative operator power $$ \gamma \ge 0$$ γ ≥ 0 on the well-posedness of the Camassa–Holm equations with fractional dissipation. It is shown that the zero-filter limit ( $$\alpha \rightarrow 0$$ α → 0 ) of the Camassa–Holm equation with fractional dissipation is the fractal Burgers equation...
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