2017/06/22 by Huimin Liu, Liu, Huimin, Xueke Pu +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Nonlinear Waves and Solitons #math.AP
paper · pdf · doi:10.48550/arxiv.1706.07313
32 pages
arxiv created 2017/06/22 · openalex publication_date 2017/06/22 · arxiv updated 2017/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the derivation of the Kadomtsev-Petviashvili (KP) equation for cold ion-acoustic wave in the long wavelength limit of the two-dimensional quantum Euler-Poisson system, under different scalings for varying directions in the Gardner-Morikawa transform. It is shown that the types of the KP equation depend on the scaled quantum parameter H>0. The QKP-I is derived for H>2, QKP-II for 0<H<2 and the dispersive-less KP (dKP) equation for the critical case H=2. The rigorous proof for these limits is given in the well-prepared initial data case, and the norm that is chosen to close the proof is anisotropic in the two directions, in accordance with the anisotropic structure of the KP equation as well as the Gardner-Morikawa transform. The results can be generalized in several directions.