Guo Lijuan, Chen Lei, Mihalache Dumitru, He Jingsong
College of Science, Nanjing Forestry University, Nanjing, Jiangsu, 210037, People's Republic of China.
Department of Theoretical Physics, Horia Hulubei National Institute for Physics and Nuclear Engineering, 077125 Bucharest-Magurele, Romania.
Phys Rev E. 2022 Jan;105(1-1):014218. doi: 10.1103/PhysRevE.105.014218.
In this paper, we first modify the binary Darboux transformation to derive three types of soliton interaction solutions of the Davey-Stewartson I equation, namely the higher-order lumps, the localized rogue wave on a solitonic background, and the line rogue wave on a solitonic background. The uniform expressions of these solutions contain an arbitrary complex constant, which plays a key role in obtaining diverse interaction scenarios. The second-order dark-lump solution contains two hollows that undergo anomalous scattering after a head-on collision, and the minimum values of the two hollows evolve in time and reach the same asymptotic constant value 0 as t→±∞. The localized rogue wave on a solitonic background describes the occurrence of a waveform from the solitonic background, quickly evolving to a doubly localized wave, and finally retreating to the solitonic background. The line rogue wave on the solitonic background does not create an extreme wave at any instant of time, unlike the one on a constant background, which has a large amplitude at the intermediate time of evolution. For large t, the solitonic background has multiple parallel solitons possessing the same asymptotic velocities and heights. The obtained results improve our understanding of the generation mechanisms of rogue waves.
在本文中，我们首先对二元达布变换进行修正，以推导Davey-Stewartson I方程的三种孤子相互作用解，即高阶团块、孤子背景上的局域怪波以及孤子背景上的线怪波。这些解的统一表达式包含一个任意复常数，该常数在获得多样的相互作用情形中起着关键作用。二阶暗团块解包含两个空洞，它们在正面碰撞后经历反常散射，并且两个空洞的最小值随时间演化，当(t→±∞)时达到相同的渐近常数(0)。孤子背景上的局域怪波描述了一种波形从孤子背景出现，迅速演化为双局域波，最后退回到孤子背景的过程。与在恒定背景上的情况不同，孤子背景上的线怪波在演化的中间时刻不会产生极端波，在恒定背景上的线怪波在演化中间时刻具有大振幅。对于大的(t)，孤子背景有多个具有相同渐近速度和高度的平行孤子。所获得的结果增进了我们对怪波产生机制的理解。
