On the Periodic Solutions of the Five-Dimensional Lorenz Equation Modeling Coupled Rosby Waves and Gravity Waves

被引：0
|
作者：
Carvalho, Tiago [1 ]
Llibre, Jaume [2 ]
机构：
[1] UNESP, Dept Matemat, Fac Ciencias, Av Eng Luiz Edmundo Carrijo Coube 14-01, BR-17033360 Bauru, SP, Brazil
[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 06期
基金：
巴西圣保罗研究基金会;
关键词：
Lorenz system; periodic solution; averaging theory; SLOW MANIFOLD; SYSTEM;
D O I：
10.1142/S0218127417500900
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Lorenz studied the coupled Rosby waves and gravity waves using the differential system (U) over dot = -VW + bVZ, (V) over dot = UW -bUZ, (W) over dot = -UV, (X) over dot = -Z, Z over dot = bUV + X. This system has the two first integrals H-1 = U-2 + V-2, H-2 = V-2 + W-2 + X-2 + Z(2). Our main result shows that in each invariant set {H-1 = h(1) > 0} boolean AND {H-2 = h(2) > 0} there are at least four (resp., 2) periodic solutions of the differential system with b not equal 0 and h(2) > h(1) (resp., h(2) < h(1)).
引用
收藏
页数：6
相关论文
共 50 条
  • [21] Three-dimensional instabilities of periodic gravity waves in shallow water
    Francius, Marc
    Kharif, Christian
    JOURNAL OF FLUID MECHANICS, 2006, 561 : 417 - 437
  • [22] Quasi-Periodic Orbits in the Five-Dimensional Nondissipative Lorenz Model: The Role of the Extended Nonlinear Feedback Loop
    Faghih-Naini, Sara
    Shen, Bo-Wen
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (06):
  • [23] Traveling, periodic and localized solitary waves solutions of the (4+1)-dimensional nonlinear Fokas equation
    Hitender Khatri
    Anand Malik
    Manjeet Singh Gautam
    SN Applied Sciences, 2020, 2
  • [24] Traveling, periodic and localized solitary waves solutions of the (4+1)-dimensional nonlinear Fokas equation
    Khatri, Hitender
    Malik, Anand
    Gautam, Manjeet Singh
    SN APPLIED SCIENCES, 2020, 2 (11):
  • [25] MODIFIED BABENKO'S EQUATION FOR PERIODIC GRAVITY WAVES ON WATER OF FINITE DEPTH
    Dinvay, E.
    Kuznetsov, N.
    QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 2019, 72 (04): : 415 - 428
  • [26] EXISTENCE OF PERIODIC-SOLUTIONS OF AN INTEGRO-DIFFERENTIAL EQUATION MODELING RESONANT WATER-WAVES
    REYNOLDS, DW
    PROCEEDINGS OF THE ROYAL IRISH ACADEMY SECTION A-MATHEMATICAL AND PHYSICAL SCIENCES, 1987, 87 (02) : 155 - 161
  • [27] Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves
    Sprenger, Patrick
    Bridges, Thomas J.
    Shearer, Michael
    JOURNAL OF NONLINEAR SCIENCE, 2023, 33 (05)
  • [28] Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves
    Patrick Sprenger
    Thomas J. Bridges
    Michael Shearer
    Journal of Nonlinear Science, 2023, 33
  • [29] Periodic solutions, breathers and rogue waves in a generalized coupled Hirota system
    Zhao, Hui-Hui
    Zhao, Xiao-Juan
    Guo, Rui
    OPTIK, 2016, 127 (20): : 9295 - 9304
  • [30] On quasi-periodic waves and rogue waves to the (4+1)-dimensional nonlinear Fokas equation
    Wang, Xiu-Bin
    Tian, Shou-Fu
    Feng, Lian-Li
    Zhang, Tian-Tian
    JOURNAL OF MATHEMATICAL PHYSICS, 2018, 59 (07)
12345