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 nonlinearity \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 wellposedness 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:

arXiv eprints
 Pub Date:
 February 2018
 DOI:
 10.48550/arXiv.1802.07345
 arXiv:
 arXiv:1802.07345
 Bibcode:
 2018arXiv180207345L
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 19 pages