Bifurcations and Oscillations for Water Waves in an EnclosedBasin

本研究项目将运用微扰方法、分岔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荡的一次分岔和二次分岔的理论和应用。物理动机是“晃动”问题，这一现象在卡车、轨道车辆、液化天然气和海上油轮、卫星等液体运输中具有巨大的实际重要性。结果表明，对水波问题解的异常分支的解释是一般的，并且可能出现在许多物理系统在特定的对称条件下。

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.