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A new nonlinear dispersive partial differential equation with cubic nonlinearity, which includes the famous Novikov equation as special case, is investigated. We first establish the local well-posedness in a range of the Besov spaces Bp,rs, p,r∈[1,∞], s>max{32,1+1p} but s≠2+1p (which generalize the Sobolev spaces Hs), well-posedness in Hs with s>32, is also established by applying Katoʼs semigroup...
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