A Class of Coupled Nonlinear Schrödinger Equation:Painlevé Property,Exact Solutions and Application to Atmospheric Gravity Waves
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摘要: 讨论了大气科学里的一类耦合非线性Schrdinger方程的Painlevé可积性和严格解.并给出了这个耦合方程通过Painlevé性质检测的参数条件.应用椭圆余弦函数展开法,得到了这个耦合非线性Schrdinger方程的20个周期椭圆余弦波解.这些严格解被用应用于解释大气重力波的产生和传输机制.
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关键词:
- 耦合非线性Schrdinger方程 /
- Painlevé 性质 /
- 严格解 /
- 大气重力波
Abstract: The Painlev? integrability and exact solutions of a coupled nonlinear Schrödinger (CNLS) equation applied in atmospheric dynamics were discussed. Some parametric restrictions of the CNLS equation were given to pass the Painlevé test. 20 periodic cnoidal wave solutions were obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions of the CNLS equation are applied to explain the generation and propagation of atmospheric gravity waves.-
Key words:
- coupled nonlinear Schrö /
- dinger equation /
- Painlevé /
- property
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[1] Huang F, Tang X Y, Lou S Y, Lu C H.Evolution of dipole-type blocking life cycle: analytical diagnoses and observations[J]. J Atmos Sci, 2007,64(1): 52-73. doi: 10.1175/JAS3819.1 [2] Li Z L. Solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere[J].J Phys A: Math Theor, 2008, 41(14): 145206. doi: 10.1088/1751-8113/41/14/145206 [3] Li Z L. Application of higher-order KdV-mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere[J].Chinese Physics B, 2009, 18(10):4074-4082. doi: 10.1088/1674-1056/18/10/003 [4] Jacobi C, Gavrilov N M, Kurschner D. Gravity wave climatology and trends in the mesosphere/lower thermosphere region deduced from low-frequency drift measurements 1984-2003[J].J Atmos and Solar-Terrestrial Phys, 2006, 68(17): 1913-1923. [5] 李子良,傅刚, 郭敬天,端义宏, 张美根. 岛屿地形对极地低压和热带气旋发展的线性理论模型和观测资料分析[J]. 应用数学和力学, 2009, 30(10): 1189-1201. [6] Liu P, Gao X N. Symmetry analysis of nonlinear incompressible non-Hydrostatic boussinesq equations[J].Commun Theor Phys, 2010, 53(4):609-614. [7] 朱利华, 周伟灿, 邹兰军. 垂直切变流中非线性重力波及其相互作用[J]. 南京气象学院学报, 2004, 27(3):405-412. [8] Benney D J, Newell A C. The propagation of nonlinear wave envelopes[J].J Math and Phys, 1967, 46(2): 133-139. [9] Tan B K. Collision interactions of envelope Rossby solitons in a barotropic atmosphere[J].J Atmos Sci,1996, 53(11): 1604-1616. doi: 10.1175/1520-0469(1996)053<1604:CIOERS>2.0.CO;2 [10] Tang X Y, Shukla P K. Solution of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrdinger equation with an external potential[J].Phys Rev A, 2007, 76(1): 013612. doi: 10.1103/PhysRevA.76.013612 [11] Pulov V I. Solutions and laws of conservation for coupled nonlinear Schrdinger equations: Lie group analysis[J].Phys Rev E, 1998, 57(3): 3468-3477. doi: 10.1103/PhysRevE.57.3468 [12] Tan B K, Ying D P. Propagation of envelope solitons in baroclinic atmosphere[J]. Advances in Atmospheric Sciences, 1995, 12(4): 439-448. doi: 10.1007/BF02657004 [13] Mattea R T, Gordon E S. Evolution of solitary marginal disturbances in baroclinic frontal geostrophic dynamics with dissipation and time-varying background flow[J].Proc R Soc A, 2007, 463(7): 1749-1769. [14] Porubov A V, Parker D F. Some general periodic solutions to coupled nonlinear Schrdinger equations[J].Wave Motion, 1999, 29(2): 97-109. [15] Sahadevan R, Tamizhmani K M, Lakshmanan M. Painlevé analysis and integrability of coupled non-linear Schrdinger equations[J]. J Phys A, 1986, 19(10): 1783-1791. [16] Radhakrishan R, Sahadevan R, Lakshmanan M. Integrability and singularity structure of coupled nonlinear Schrdinger equations[J].Chaos, Solitons & Fractals, 1995, 5(12): 2315-2327. [17] Kanna T, Lakshmanan M. Exact soliton solutions of coupled nonlinear Schrdinger equations: shape-changing collisions, logic gates, and partially coherent solitons[J]. Phys Rev E, 2003, 67 (4): 046617. [18] Liu P, Lou S Y. Coupled nonlinear Schrdinger equation: symmetries and exact solutions[J].Commun Theor Phys, 2009, 51(1): 27-34. [19] Painlevé P. Sur les équations différentielles du premier ordre[J]. C R Acas Soc Paris, 1888, 107: 221-224. [20] Ablowitz M J, Ramani A, Segur H. A connection between nonlinear evolution equations and ordinary differential equations of P-type[J].J Math. Phys, 1980, 21(5): 1006-1015. [21] Weiss J, Tabor M, Carnevale G. The Painlevé property for partial differential equations[J]. J Math Phys, 1983, 24(3): 522-526. doi: 10.1063/1.525721 [22] Jimbo, M, Kruskal M D, Miwa T. Painlevé test for self-dual Yang-Mills equation[J]. Phys Lett A, 1982, 92(2): 59-60. doi: 10.1016/0375-9601(82)90291-2 [23] Conte R. Invariant Painlevé analysis of partial differential equations[J].Phys Lett A, 1989, 140(7/8): 383-390. [24] Lou S Y. Extended Painlevé expansion, nonstand truncation and special reductions of nonlinear evolution equations[J]. Z Naturforsch A, 1998, 53(5): 251-258. [25] Liu P, Lou S Y. Lie point symmetries and exact solutions of the coupled volterra system[J].Chin Phys Lett, 2010, 27(2): 020202. doi: 10.1088/0256-307X/27/2/020202 [26] Liu P, Lou S Y. A(2+1)-dimensional displacement shallow water wave system[J].Chin Phys Lett, 2008, 25(9): 3311-3314. [27] 刘式适, 付遵涛, 刘式达, 赵强.求某些非线性偏微分方程特解的一个简洁方法[J]. 应用数学和力学, 2001, 22(3): 281-286. [28] 许习华,丁一汇. 中尺度大气运动中孤立重力波特征的研究[J]. 大气科学, 1991,15(4):58-68. [29] 寿绍文,励申申,姚秀萍. 中尺度气象学[M]. 北京:气象出版社, 2003.
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