Persistence property and infinite propagation speed for the b-family of Fokas-Olver-Rosenau-Qiao (bFORQ) model

Abstract In this paper, we study the b -family of Fokas–Olver–Rosenau–Qiao ( b FORQ) model. We discuss the persistence property in weighted Sobolev spaces. The infinite propagation speed is also investigated. We prove that the strong solution u ( x , t ) does not have compact x -support for any t > 0 in its lifespan, although the corresponding u 0 ( x ) is compactly supported. We also present a special property that if the initial datum m 0 ( x ) ⁄ ≡ 0 is compactly supported in [ a , c ] , then the endpoints do not move by the characteristic line.

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