Asymptotic dynamics of higher-order lumps in the Davey–Stewartson II equation

A family of higher-order rational lumps on non-zero constant background Davey-Stewartson (DS) II equation are investigated. These solutions have multiple peaks whose heights and trajectories approximately given by asymptotical analysis. It is found that the time-dependent for large time they approach same height value first-order fundamental lump. The resulting considered it scattering angle can assume arbitrary values in interval $(\frac{\pi}{2}, \pi)$ which markedly distinct from necessary orthogonal zero background. Additionally, illustrated containing multi-peaked $n$-lumps be regarded as a nonlinear superposition $n$ ones $|t|\rightarrow\infty$.