| Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere |
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| 引用本文： | 李子良. Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere[J]. 中国物理 B, 2009, 18(10): 4074-4082. DOI: 10.1088/1674-1056/18/10/003 |
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| 作者姓名： | 李子良 |
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| 作者单位： | Department of Marine Meteorology, Laboratory of Air-Sea Interaction and Climate, Ocean University of China, Qingdao 266100, China |
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| 基金项目： | Projectsupported by the National Natural Science Foundation ofChina (Grant No 40775069). |
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| 摘 要： | Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equationswith a higher-degree of nonlinear terms are derived from a simpleincompressible non-hydrostatic Boussinesq equation set in atmosphereand are used to investigate gravity waves in atmosphere. By takingadvantage of the auxiliary nonlinear ordinary differential equation,periodic wave and solitary wave solutions of the fifth-orderKdV--mKdV models with higher-degree nonlinear terms are obtainedunder some constraint conditions. The analysis shows that thepropagation and the periodic structures of gravity waves depend onthe properties of the slope of line of constant phase and atmosphericstability. The Jacobi elliptic function wave and solitary wavesolutions with slowly varying amplitude are transformed intotriangular waves with the abruptly varying amplitude and breakinggravity waves under the effect of atmospheric instability.
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| 关 键 词： | gravity waves higher-order KdV-mKdV equation propagating breaking |
| 收稿时间： | 2009-01-31 |
Application of higher-order KdV--mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere |
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| Li Zi-Liang. 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 |
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| Authors: | Li Zi-Liang |
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| Affiliation: | Department of Marine Meteorology, Laboratory of Air-Sea Interaction and Climate, Ocean University of China, Qingdao 266100, China |
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| Abstract: | Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equationswith a higher-degree of nonlinear terms are derived from a simpleincompressible non-hydrostatic Boussinesq equation set in atmosphereand are used to investigate gravity waves in atmosphere. By takingadvantage of the auxiliary nonlinear ordinary differential equation,periodic wave and solitary wave solutions of the fifth-orderKdV--mKdV models with higher-degree nonlinear terms are obtainedunder some constraint conditions. The analysis shows that thepropagation and the periodic structures of gravity waves depend onthe properties of the slope of line of constant phase and atmosphericstability. The Jacobi elliptic function wave and solitary wavesolutions with slowly varying amplitude are transformed intotriangular waves with the abruptly varying amplitude and breakinggravity waves under the effect of atmospheric instability. |
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| Keywords: | gravity waves higher-orderKdV--mKdV equation propagating breaking |
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