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arXiv · 2303.10745

A semi-periodic initial-value problem for the Kadomtsev-Petviashvili II equation

P. Kalamvokas·V. G. Papageorgiou·A. S. Fokas·L. -Y. Sung
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Abstract

We investigate the Cauchy problem on the cylinder, namely the semi-periodic problem where there is periodicity in the $x$-direction and decay in the $y$-direction, for the Kadomtsev-Petviashvili II equation by the inverse spectral transform method. For initial data with small $L^1$ and $L^2$ 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.

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P. Kalamvokas, V. G. Papageorgiou, A. S. Fokas, L. -Y. Sung. 2023-03-19. A semi-periodic initial-value problem for the Kadomtsev-Petviashvili II equation. https://arxiv.org/abs/2303.10745

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