Application of higher-order KdV-mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

• 来源期刊: 中国物理B（英文版）
• 关键词: gravity waves higher-order KdV-mKdV equation propagating breaking
• 年，卷（期）: 2009,（10）
• 页码范围: 4074-4082
• 页数: 9页
• 语种: 英文

摘要

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.