English

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 xx-direction and decay in the yy-direction, for the Kadomtsev-Petviashvili II equation by the inverse spectral transform method. For initial data with small L1L^1 and L2L^2 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}
}