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arXiv · 1802.07345

On a class of solutions to the generalized KdV type equation

Felipe Linares·Hayato Miyazaki·Gustavo Ponce
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Abstract

We consider the IVP associated to the generalized KdV equation with low degree of non-linearity \begin{equation*} \partial_t u + \partial_x^3 u \pm |u|^{\alpha}\partial_x u = 0,\; x,t \in \mathbb{R},\;\alpha \in (0,1). \end{equation*} By using an argument similar to that introduced by Cazenave and Naumkin [2] 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 [3] in solutions of the $k$-generalized KdV equation.

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Felipe Linares, Hayato Miyazaki, Gustavo Ponce. 2018-02-20. On a class of solutions to the generalized KdV type equation. https://doi.org/10.1142/s0219199718500566

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