Bifurcations and Oscillations for Water Waves in an EnclosedBasin

本研究项目将利用摄动方法、分叉理论和其他先进的数学技术，发展封闭矩形盆地中水波非线性振动的一次分叉和二次分叉的理论和应用。物理动因是“晃动”问题，这是一种在卡车、轨道车、LNG&Amp；油轮、卫星等液体运输中具有极大实际意义的现象。结果表明，对水波问题解的异常分支的解释是通用的，在特定对称条件下可能出现在许多物理系统中。

This research project will develop the theory and application of the primary and secondary bifurcation of nonlinear oscillations of water waves in enclosed rectangular basins using perturbation methods, bifurcation theory, and other advanced mathematical techniques. The physical motivation is the "sloshing" problem, a phenomena of tremendous practical importance in liquid transport in trucks, rail cars, LNG & oil sea tankers, satellites, etc. The results indicate that explanation for the anomalous branches of solutions in the water wave problem are generic and may occur in many physical systems under particular symmetry conditions.