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| 摘要: |
| 本文研究了小展弦比波的Green-Naghdi渐进模型. 利用平面自治系统的稳定性分析方法, 在不同的参数条件下, 讨论了它的行波系统的分岔并且给出了对应的相图, 得到了光滑周期波解, 广义扭波解, 广义反扭波解, 广义紧波解, 周期尖波解, 孤波解和孤立尖波解的精确表达式. 进一步, 通过数学软件Maple模拟了这些解. |
| 关键词: Green-Naghdi渐进模型 行波解 相图 分岔 |
| DOI： |
| 分类号:O175.24 |
| 基金项目:Supported by the Natural Science Foundation of Zhanjiang Normal University (L1104 and LZL1101); the Natural Science Foundation of Guangdong Province (S2013010015957). |
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| TRAVELING WAVE SOLUTIONS OF A GREEN-NAGHDI ASYMPTOTIC MODEL FOR SMALL ASPECT RATIO WAVES |
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ZHONG Ji-yu,LI Xiao-pei
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| Abstract: |
| A Green-Naghdi asymptotic model for small aspect ratio waves is investigated by qualitative analysis methods of planar autonomous systems. Under different parameter conditions, the bifurcation of its traveling wave system is discussed and the corresponding phase portraits are also given. The exact expressions of some bounded traveling wave solutions are obtained, such as smooth periodic wave solutions, kink-like wave solutions, antikink-like wave solutions, compacton-like wave solutions, periodic cusp wave solutions, solitary wave solutions and cusp solitary wave solutions. Furthermore, these solutions are simulated by applying the software Maple. |
| Key words: Green-Naghdi asymptotic model traveling wave solutions phase portraits bi-furcations |
