Local well-posedness in weighted Sobolev spaces for nonlinear dispersive equations with applications to dispersive blow up

In the first part of this work we study the local well-posedness of dispersive equations in the weighted spaces H(R) ∩ L(|x|dx). We then apply our results for several dispersive models such as the Hirota-Satsuma system, the OST equation, the Kawahara equation and a fifth-order model. Using these local results, the second part of this work is devoted to obtain results related to dispersive blow up of the Kawahara equation and Hirota-Satsuma system.

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