Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (5): 883-892.
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Danni Wang,Hongli Yang*(),Liangui Yang
Received:
2016-07-13
Online:
2018-11-09
Published:
2018-11-09
Contact:
Hongli Yang
E-mail:hongliyang3@sohu.com
Supported by:
CLC Number:
Danni Wang,Hongli Yang,Liangui Yang. Derivation of a Higher Order Nonlinear Schrödinger Equation with Complete Coriolis Force[J].Acta mathematica scientia,Series A, 2018, 38(5): 883-892.
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1 |
Long R R , Andrushkiw R I , Huang X H . Solitary waves in the Westerlies. J Atmos Sci, 1964, 21: 197- 200
doi: 10.1175/1520-0469(1964)021<0197:SWITW>2.0.CO;2 |
2 |
Benney D J . Long nonlinear waves in fluid flows. J Math Phys, 1966, 45: 52- 63
doi: 10.1002/sapm196645152 |
3 |
Redekopp L G . On the theory of solitary Rossby waves. J Fluid Meth, 1977, 82: 725- 745
doi: 10.1017/S0022112077000950 |
4 |
Boyd J P . Equatorial solitary waves. Part Ⅰ:Rossby solitons. J Phys Ocean, 1980, 10 (11): 1699- 1718
doi: 10.1175/1520-0485(1980)010<1699:ESWPIR>2.0.CO;2 |
5 |
Grimshaw R H J . Evolution equations for long, nonlinear internal waves in stratified shear flows. Stud Appl Math, 1981, 65: 159- 188
doi: 10.1002/sapm.v65.2 |
6 |
Yang H W , Yin B S , Yang D I , Xu Z H . Forced solitary Rossby waves under the influence of slowly varying topography with time. Chin Phys B, 2011, 20 (12): 120201
doi: 10.1088/1674-1056/20/12/120201 |
7 |
Benney D J . Large amplitude Rossby waves. Stud Appl Math, 1979, 60: 1- 10
doi: 10.1002/sapm.v60.1 |
8 |
Yamagata T . The stability, modulation and long wave resonance of a planetary wave in a rotating, two-layer fluid on a channel beta-plane. J Meteorol Soc Japan, 1980, 58: 160- 171
doi: 10.2151/jmsj1965.58.3_160 |
9 |
Bao W , Jaksch D , Markowich P . Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation. J Comput Phys, 2003, 187 (1): 318- 342
doi: 10.1016/S0021-9991(03)00102-5 |
10 | Bao W , Cai Y . Mathematical theory and numerical methods for Bose-Einstein condensation Kinet. Relat Mod, 2013, 6: 1- 135 |
11 | Liang X , Khaliq A , Sheng Q . Exponential time differencing Crank-Nicolson method with a quartic spline approdinger for nonlinear Schrödinger equations. Appl Math Comput, 2014, 235: 235- 252 |
12 |
Sheng Q , Khaliq A , Al-Said E . Solving the generalized nonlinear Schröginger equation via quartic spline approximation. J Comput Phys, 2001, 166 (2): 400- 417
doi: 10.1006/jcph.2000.6668 |
13 | Peng C Q , Ma S C . The existence of nontrivial solutions for a class of asymtotically linear equation. Acta Mathematica Scientia, 2013, 33A (6): 1035- 1044 |
14 | Xu N , Ma S W . Ground state sulutions for periodic Schrödinger equation with critical sobolev exponent. Acta Mathematica Scientia, 2015, 35A (4): 651- 655 |
15 | Wei G M , Li Q . Mountain pass solutions for fractional coupled nonlinear Schrödinger systems. Acta Mathematica Scientia, 2016, 36A (1): 65- 79 |
16 |
Cai W , Wang Y , Song Y . Numerical simulation of Rogue waves by the local discontinuous galerkin method. Chin Phys Lett, 2014, 31 (4): 040201
doi: 10.1088/0256-307X/31/4/040201 |
17 |
Liao C C , Cui J C , Liang J Z , Ding X H . Muilti-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients. Chin Phy B, 2016, 25 (1): 010205
doi: 10.1088/1674-1056/25/1/010205 |
18 | Chen J C , Li B , Chen Y . Novel exact solutions of coupled nonlinear Schrödinger equations with time-space modulation. Chin Phy B, 2013, 11: 110306 |
19 | Yao Z A . Homogenization of some linear and semilinear Schrödinger equations with real potential. Acta Mathematica Scientia, 2001, 21B (1): 137- 144 |
20 |
Li J W , Fang N W , Zhang J , et al. (2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect. Chin Phy B, 2016, 25 (4): 040202
doi: 10.1088/1674-1056/25/4/040202 |
21 |
Luo D H . Derivation of a higher order nonlinear Schrödinger equation for weakly nonlinear Rossby waves. Wave Motion, 2001, 33: 339- 347
doi: 10.1016/S0165-2125(00)00073-1 |
22 |
Li Z D , Wu X , Li Q Y , He P B . Kuznetsov-Masoltion and Akhmediev breather of high-order nonlinear Schrödinger equation. Chin Phy B, 2016, 25 (1): 010507
doi: 10.1088/1674-1056/25/1/010507 |
23 |
Philips N A . The equations of motion for a shallow rotating atmosphere and 'traditional approximation'. J Atmos Sci, 1966, 23 (5): 626- 628
doi: 10.1175/1520-0469(1966)023<0626:TEOMFA>2.0.CO;2 |
24 |
Veronis G . Comments on Phillips' (1966) proposed simplification of the equations of motion for shallow rotating atmosphere. J Atmos Sci, 1968, 25 (6): 1154- 1155
doi: 10.1175/1520-0469(1968)025<1154:COPPSO>2.0.CO;2 |
25 |
Wangness R K . Comment on "The equations of motion for a shallow rotating atmosphere and the 'traditional approxmation'". J Atmos Sci, 1970, 27 (3): 504- 506
doi: 10.1175/1520-0469(1970)027<0504:COEOMF>2.0.CO;2 |
26 |
Leibovich S , Lele S K . The influence of the horizonal component of the Erath's angular velocity on the instability of the Ekman layer. Journal of Fluid Mechanics, 1985, 150: 41- 87
doi: 10.1017/S0022112085000039 |
27 | Draghici I . Non-hydrostatic Coriolis effects in an isentropic coordinate frame. Russian Meteorology and Hydrology, 1987, 17: 45- 54 |
28 |
Sun W Y . Unsymmetrical symmetric instability. Quarterly Journal of the Royal Meteorological Society, 1995, 121: 419- 431
doi: 10.1002/(ISSN)1477-870X |
29 |
White A A , Bromely R A . Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Quarterly Journal of the Royal Meteorological Society, 1995, 121: 399- 418
doi: 10.1002/(ISSN)1477-870X |
30 | Burger A P . The potential vorticity equation:from planetary to small scale. Tellus, 1991, 43A: 191- 197 |
31 |
赵强, 于鑫. 完整Coriolis力作用下非线性Rossby波的精确解. 地球物理学报, 2008, 51 (5): 1304- 1308
doi: 10.3321/j.issn:0001-5733.2008.05.004 |
Zhao Q , Yu X . Exact solutions to the nonlinear Rossby waves with a complete representation of the Coriolis force. Chinese Journal of Geophysics, 2008, 51 (5): 1304- 1308
doi: 10.3321/j.issn:0001-5733.2008.05.004 |
|
32 | 宋健, 刘全生, 杨联贵. 缓变地形下β效应的Rossby代数孤立波. 地球物理学进展, 2013, 28 (4): 1684- 1688 |
Song J , Liu Q S , Yang L G . Algebraic solitary Rossby waves excited slowly changing topography and beta effect. Progress in Geophysics, 2013, 28 (4): 1684- 1688 | |
33 | Dellar P J , Salomon R . Shallow water equations with a copplete Coriolis force and topography. J Fluid Mech, 2005, 17: 106601 |
34 | Plumb R A . The stability of small amplitude Rossby waves in a channel. Stud Appl Math, 1977, 80 (4): 705- 720 |
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