Abstract Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV--mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.
Received: 31 January 2009
Revised: 14 May 2009
Accepted manuscript online:
PACS:
92.60.hh
(Acoustic gravity waves, tides, and compressional waves)
Fund: Project
supported by the National Natural Science Foundation of
China (Grant No 40775069).
Cite this article:
Li Zi-Liang(李子良) Application of higher-order KdV--mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere 2009 Chin. Phys. B 18 4074
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