[1] |
Benney D J. 1966. Long non-linear waves in fluid flows. Journal of Mathematics and Physics, 45(1–4): 52–63 |
[2] |
Caillol P, Grimshaw R H. 2008. Rossby elevation waves in the presence of a critical layer. Studies in Applied Mathematics, 120(1): 35–64 |
[3] |
Caldwell D R. 1983. Small-scale physics of the ocean. Reviews of Geophysics, 21(5): 1192–1205 |
[4] |
Fruman M D. 2009. Equatorially bounded zonally propagating linear waves on a generalized β plane. Journal of the Atmospheric Sciences, 66(9): 2937–2945 |
[5] |
Fu Lei, Chen Yaodeng, Yang Hongwei. 2019. Time-space fractional coupled generalized Zakharov-Kuznetsov equations set for Rossby solitary waves in two-layer fluids. Mathematics, 7(1): 41 |
[6] |
Fu Lei, Yang Hongwei. 2019. An application of (3+1)-dimensional time-space fractional ZK model to analyze the complex dust acoustic waves. Complexity, 2019: 2806724 |
[7] |
Gerkema T, Shrira V I. 2005a. Near-inertial waves on the “nontraditional” β plane. Journal of Geophysical Research: Oceans, 110(C1): C01003 |
[8] |
Gerkema T, Shrira V I. 2005b. Near-inertial waves in the ocean: Beyond the “traditional approximation”. Journal of Fluid Mechanics, 529: 195–219 |
[9] |
Gerkema T, Zimmerman J T F, Maas L R M, et al. 2008. Geophysical and astrophysical fluid dynamics beyond the traditional approximation. Reviews of Geophysics, 46(2): RG2004 |
[10] |
Grimshaw R H J. 1975. A note on the β-plane approximation. Tellus, 27(4): 351–357 |
[11] |
Guo Min, Dong Haoyu, Liu Jianxin, et al. 2019. The time-fractional mZK equation for gravity solitary waves and solutions using sech-tanh and radial basic function method. Nonlinear Analysis: Modelling and Control, 24(1): 1–19 |
[12] |
Hayashi M, Itoh H. 2012. The importance of the nontraditional Coriolis terms in large-scale motions in the tropics forced by prescribed cumulus heating. Journal of the Atmospheric Sciences, 69(9): 2699–2716 |
[13] |
Helal M A, Seadawy A R. 2012. Benjamin-Feir instability in nonlinear dispersive waves. Computers & Mathematics with Applications, 64(11): 3557–3568 |
[14] |
Holton J R, Hakim G J. 2013. An Introduction to Dynamic Meteorology. 5th ed. Boston: Academic Press |
[15] |
Itano T, Kasahara A. 2011. Effect of top and bottom boundary conditions on symmetric instability under full-component Coriolis force. Journal of the Atmospheric Sciences, 68(11): 2771–2782 |
[16] |
Kasahara A. 2003. On the nonhydrostatic atmospheric models with inclusion of the horizontal component of the earth’s angular velocity. Journal of the Meteorological Society of Japan. Ser. Ⅱ, 81(5): 935–950 |
[17] |
Kasahara A. 2010. A mechanism of deep-ocean mixing due to near-inertial waves generated by flow over bottom topography. Dynamics of Atmospheres and Oceans, 49(2–3): 124–140 |
[18] |
Khater A H, Callebaut D K, Helal M A, et al. 2006a. Variational method for the nonlinear dynamics of an elliptic magnetic stagnation line. The European Physical Journal D-Atomic, Molecular, Optical and Plasma Physics, 39(2): 237–245 |
[19] |
Khater A H, Callebaut D K, Seadawy A R. 2006b. General soliton solutions for nonlinear dispersive waves in convective type instabilities. Physica Scripta, 74(3): 384–393 |
[20] |
Kloosterziel R C, Carnevale G F, Orlandi P. 2007. Inertial instability in rotating and stratified fluids: barotropic vortices. Journal of Fluid Mechanics, 583: 379–412 |
[21] |
Kloosterziel R C, Carnevale G F, Orlandi P. 2017. Equatorial inertial instability with full Coriolis force. Journal of Fluid Mechanics, 825: 69–108 |
[22] |
Leibovich S, Lele S K. 1985. The influence of the horizontal component of earth’s angular velocity on the instability of the Ekman layer. Journal of Fluid Mechanics, 150: 41–87 |
[23] |
Liu Yongjun, Gao Xiaoping, Yu Tianxia, et al. 2015. Influence of complete Coriolis force on the dispersion relation of ocean internal-wave in a background currents field. MATEC Web of Conferences, 25: 01014 |
[24] |
Long R R. 1964. Solitary waves in the westerlies. Journal of the Atmospheric Sciences, 21(2): 197–200 |
[25] |
Marshall J, Schott F. 1999. Open-ocean convection: Observations, theory, and models. Reviews of Geophysics, 37(1): 1–64 |
[26] |
Nezlin M V, Snezhkin E N. 1993. Rossby Vortices, Spiral Structures, Solitons. Berlin: Springer-Verlag |
[27] |
Ono H. 1981. Algebraic Rossby wave soliton. Journal of the Physical Society of Japan, 50(8): 2757–2761 |
[28] |
Pedlosky J. 1987. Geophysical Fluid Dynamics. New York: Springer-Verlag |
[29] |
Phillips N A. 1966. The equations of motion for a shallow rotating atmosphere and the “traditional approximation”. Journal of the Atmospheric Sciences, 23(5): 626–628 |
[30] |
Ren Yanwei, Tao Mengshuang, Dong Huanhe, et al. 2019. Analytical research of (3+1)-dimensional Rossby waves with dissipation effect in cylindrical coordinate based on Lie symmetry approach. Advances in Difference Equations, 2019: 13 |
[31] |
Satsuma J, Ablowitz M J, Kodama Y. 1979. On an internal wave equation describing a stratified fluid with finite depth. Physics Letters A, 73(4): 283–286 |
[32] |
Seadawy A R. 2011. New exact solutions for the KdV equation with higher order nonlinearity by using the variational method. Computers & Mathematics with Applications, 62(10): 3741–3755 |
[33] |
Seadawy A R. 2015. Nonlinear wave solutions of the three-dimensional Zakharov-Kuznetsov-Burgers equation in dusty plasma. Physica A: Statistical Mechanics and its Applications, 439: 124–131 |
[34] |
Seadawy A R. 2016. Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a magnetized electron-positron plasma. Physica A: Statistical Mechanics and its Applications, 455: 44–51 |
[35] |
Seadawy A R. 2017a. Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods. The European Physical Journal Plus, 132(12): 518 |
[36] |
Seadawy A R. 2017b. Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas. Pramana, 89(3): 49 |
[37] |
Seadawy A R. 2018. Three-dimensional weakly nonlinear shallow water waves regime and its traveling wave solutions. International Journal of Computational Methods, 15(3): 1850017 |
[38] |
Seadawy A R, Alamri S Z. 2018. Mathematical methods via the nonlinear two-dimensional water waves of Olver dynamical equation and its exact solitary wave solutions. Results in Physics, 8: 286–291 |
[39] |
Seadawy A R, Lu D C, Yue C. 2017. Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability. Journal of Taibah University for Science, 11(4): 623–633 |
[40] |
Tian Runhua, Fu Lei, Ren Yanwei, et al. 2019. (3+1)-Dimensional time-fractional modified Burgers equation for dust ion-acoustic waves as well as its exact and numerical solutions. Mathematical Methods in the Applied Science, 1–20 |
[41] |
Tort M, Ribstein B, Zeitlin V. 2016. Symmetric and asymmetric inertial instability of zonal jets on the f-plane with complete Coriolis force. Journal of Fluid Mechanics, 788: 274–302 |
[42] |
White A A, Bromley R A. 1995. Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Quarterly Journal of the Royal Meteorological Society, 121(522): 399–418 |
[43] |
Yang Hongli, Liu Fumei, Wang Danni, et al. 2016. Nonlinear Rossby waves near the equator with complete Coriolis force. Progress in Geophysics (in Chinese), 31(3): 988–991 |
[44] |
Yang Hongwei, Sun Junchao, Fu Chen. 2019. Time-fractional Benjamin-Ono equation for algebraic gravity solitary waves in baroclinic atmosphere and exact multi-soliton solution as well as interaction. Communications in Nonlinear Science and Numerical Simulation, 71: 187–201 |
[45] |
Yano J I. 2017. Inertio-gravity waves under the non-traditional f-plane approximation: Singularity in the large-scale limit. Journal of Fluid Mechanics, 810: 475–488 |
[46] |
Yasuda Y, Sato K. 2013. The effect of the horizontal component of the angular velocity of the earth’s rotation on inertia-gravity waves. Journal of the Meteorological Society of Japan. Ser Ⅱ, 91(1): 23–41 |
[47] |
Zhang Xiaoming. 1991. A model of the equatorial deep jets and the role of the horizontal Coriolis parameter [dissertation]. Woods Hole: Woods Hole Oceanographic Institution |
[48] |
Zhang Ruigang, Liu Quansheng, Yang Liangui, et al. 2019a. Nonlinear planetary-synoptic wave interaction under generalized beta effect and its solutions. Chaos, Solitons & Fractals, 122: 270–280 |
[49] |
Zhang Ruigang, Yang Liangui. 2019. Nonlinear Rossby waves in zonally varying flow under generalized beta approximation. Dynamics of Atmospheres and Oceans, 85: 16–27 |
[50] |
Zhang Ruigang, Yang Liangui, Liu Quansheng, et al. 2019b. Dynamics of nonlinear Rossby waves in zonally varying flow with spatial-temporal varying topography. Applied Mathematics and Computation, 346: 666–679 |