Abstract
We consider the IVP associated to the generalized KdV equation with low degree of nonlinearity [Formula: see text] By using an argument similar to that introduced by Cazenave and Naumkin [Local existence, global existence, and scattering for the nonlinear Schrödinger equation, Commun. Contemp. Math. 19(2) (2017) 1650038, MR3611666], we establish the local well-posedness for a class of data in an appropriate weighted Sobolev space. Also, we show that the solutions obtained satisfy the propagation of regularity principle proven in [P. Isaza, F. Linares and G. Ponce, On the propagation of regularity and decay of solutions to the [Formula: see text]-generalized Korteweg–de Vries equation, Comm. Partial Differential Equations 40(7) (2015) 1336–1364, MR3341207] in solutions of the [Formula: see text]-generalized KdV equation.
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