The Cauchy problem for the Pavlov equation
Exactly Solvable and Integrable Systems
2014-07-17 v2
Abstract
Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data.
Cite
@article{arxiv.1310.5834,
title = {The Cauchy problem for the Pavlov equation},
author = {P. G. Grinevich and P. M. Santini and D. Wu},
journal= {arXiv preprint arXiv:1310.5834},
year = {2014}
}
Comments
In the new version the analytical technique was essentially revised. The previous version contained a wrong statement about the solvability of the inverse problem for large data. This problem remains open