A semi-periodic initial-value problem for the Kadomtsev-Petviashvili II equation
Analysis of PDEs
2023-03-21 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We investigate the Cauchy problem on the cylinder, namely the semi-periodic problem where there is periodicity in the -direction and decay in the -direction, for the Kadomtsev-Petviashvili II equation by the inverse spectral transform method. For initial data with small and norms, assuming the zero mass constraint, this initial-value problem is reduced to a Riemann-Hilbert problem on the boundary of certain infinite strips with shift.
Keywords
Cite
@article{arxiv.2303.10745,
title = {A semi-periodic initial-value problem for the Kadomtsev-Petviashvili II equation},
author = {P. Kalamvokas and V. G. Papageorgiou and A. S. Fokas and L. -Y. Sung},
journal= {arXiv preprint arXiv:2303.10745},
year = {2023}
}