Lee-Huang-Yang修正偶极Gross-Pitaevskii方程驻波解的强不稳定性
Strong Instability of Standing Waves for the Lee-Huang-Yang Corrected Dipolar Gross-Pitaevskii Equation
DOI: 10.12677/PM.2023.137203, PDF, 下载: 163  浏览: 462 
作者: 邓成德：西北师范大学数学与统计学院，甘肃 兰州
关键词: Gross-Pitaevskii方程；强不稳定性；爆破准则；Gross-Pitaevskii Equation； Strong Instability； Blow-Up Criterion
摘要: 考虑Lee-Huang-Yang修正偶极Gross-Pitaevskii 方程驻波解的强不稳定性当λ3 < 0和4/3 ≤ q < 4时，建立爆破准则，获得了强不定驻波解的存在性。
Abstract: The author considered the strong instability of standing waves for the Lee-Huang-Yang corrected dipolar Gross-Pitaevskii equation When λ3 < 0 and 4/3 ≤ q < 4, the author obtained the existence of strongly unstable standing waves by establishing blow-up criterion.
文章引用：邓成德. Lee-Huang-Yang修正偶极Gross-Pitaevskii方程驻波解的强不稳定性[J]. 理论数学, 2023, 13(7): 1966-1975. https://doi.org/10.12677/PM.2023.137203

参考文献

[1] Feng, B.H. and Wang, Q.X. (2021) Strong Instability of Standing Waves for the Nonlinear Schrodinger Equation in Trapped Dipolar Quantum Gases. Journal of Dynamics and Differential Equations, 33, 1989-2008.
https://doi.org/10.1007/s10884-020-09881-0
[2] Yi, S. and You, L. (2000) Trapped Atomic Condensates with Anisotrpic Interactions. Physical Review A, 61, Article 041604.
https://doi.org/10.1103/PhysRevA.61.041604
[3] Luo, Y.M. and Stylianou, A. (2021) Ground States for a Nonlocal Mixed Order Cubic-Quartic Gross-Pitaevskii Equation. Journal of Mathematical Analysis and Applications, 496, Article 124802.
https://doi.org/10.1016/j.jmaa.2020.124802
[4] Antonelli, P. and Sparber, C. (2011) Existence of Solitary Waves in Dipolar Quantum Gases. Physica D. Nonlinear Phenomena, 240, 426-431.
https://doi.org/10.1016/j.physd.2010.10.004
[5] Bao, W.Z. and Cai, Y.Y. (2013) Mathematical Theory and Numerical Methods for Bose- Einstein Condensation. Kinetic and Related Models, 6, 1-135.
https://doi.org/10.3934/krm.2013.6.1
[6] Bao, W.Z., Cai, Y.Y. and Wang, H.Q. (2010) Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates. Journal of Computational Physics, 229, 7874-7892. https://doi.org/10.1016/j.jcp.2010.07.001
[7] Bellazzini, J. and Forcella, L. (2019) Asymptotic Dynamic for Dipolar Quantum Gases below the Ground State Energy Threshold. Journal of Functional Analysis, 277, 1958-1998.
https://doi.org/10.1016/j.jfa.2019.04.005
[8] Bellazzini, J. and Jeanjean, L. (2016) On Dipolar Quantum Gases in the Unstable Regime. SIAM Journal on Mathematical Analysis, 48, 2028-2058.
https://doi.org/10.1137/15M1015959
[9] Zhang, J. (2005) Sharp Threshold for Blowup and Global Existence in Nonlinear Schrodinger Equations under a Harmonic Potential. Communications in Partial Differential Equations, 30, 1429-1443.
https://doi.org/10.1080/03605300500299539
[10] Ohta, M. (2018) Strong Instability of Standing Waves for Nonlinear Schrodinger Equations with Harmonic Potential. Funkcialaj Ekvacioj. Serio Internacia, 61, 135-143.
https://doi.org/10.1619/fesi.61.135
[11] Dinh, V.D. (2021) On the Instability of Standing Waves for 3D Dipolar Bose-Einstein Condensates. Physica D, 419, Article 132856.
https://doi.org/10.1016/j.physd.2021.132856
[12] Feng, B.H., Cao, L.J. and Liu, J.Y. (2021) Existence of Stable Standing Waves for the Lee-Huang-Yang Corrected Dipolar Gross-Pitaevskii Equation. Applied Mathematics Letters, 115, Article 106952.
https://doi.org/10.1016/j.aml.2020.106952

为你推荐