On a class of solutions to the generalized KdV type equation
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2018
- DOI:
- 10.48550/arXiv.1802.07345
- arXiv:
- arXiv:1802.07345
- Bibcode:
- 2018arXiv180207345L
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 19 pages