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It has been shown that the Cauchy problem for the Fokas–Olver–Rosenau–Qiao equation is well-posed for initial data $$u_0\in H^s$$ u 0 ∈ H s , $$s>5/2$$ s > 5 / 2 , with its data-to-solution map $$u_0\mapsto u$$ u 0 ↦ u being continuous but not uniformly continuous. This work further investigates the continuity properties of the solution map and shows that...
It is shown that the initial value problem for the Fokas–Olver–Rosenau–Qiao equation (FORQ) is well-posed in Sobolev spaces Hs, s>5/2, in the sense of Hadamard. Furthermore, it is proved that the dependence on initial data is sharp, i.e. the data-to-solution map is continuous but not uniformly continuous. Also, peakon travelling wave solutions are derived on both the circle and the line and are...
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