论文标题
Davey-Stewartson II方程中高阶团块的渐近动力学
Asymptotic dynamics of higher-order lumps in the Davey-Stewartson II equation
论文作者
论文摘要
研究了一个高阶合理团块在戴维·史图尔森（DS）II方程的非零恒定背景上的一家家族。这些溶液具有多个峰，其高度和轨迹大约通过渐近分析给出。发现高度是时间依赖的，并且在很长的时间内它们接近一阶基块的相同恒定高度值。考虑了所得的轨迹，发现散射角可以在$（\fracπ{2}，π）$的间隔中假设任意值，这与零背景上的高阶块的必要正交散射明显不同。此外，可以说的是，包含多峰$ n $ lumps的高阶团块可以被视为$ n $一阶的非线性叠加，为$ | t | \ rightarrow \ rightarrow \ infty $。
A family of higher-order rational lumps on non-zero constant background of Davey-Stewartson (DS) II equation are investigated. These solutions have multiple peaks whose heights and trajectories are approximately given by asymptotical analysis. It is found that the heights are time-dependent and for large time they approach the same constant height value of the first-order fundamental lump. The resulting trajectories are considered and it is found that the scattering angle can assume arbitrary values in the interval of $(\fracπ{2}, π)$ which is markedly distinct from the necessary orthogonal scattering for the higher-order lumps on zero background. Additionally, it is illustrated that the higher-order lumps containing multi-peaked $n$-lumps can be regarded as a nonlinear superposition of $n$ first-order ones as $|t|\rightarrow\infty$.
