Yang Bo, Yang Jianke
School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China.
Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05405, USA.
Chaos. 2024 Jul 1;34(7). doi: 10.1063/5.0210867.
We report new rogue wave patterns whose wave crests form closed or open curves in the spatial plane, which we call rogue curves, in the Davey-Stewartson I equation. These rogue curves come in various striking shapes, such as rings, double rings, and many others. They emerge from a uniform background (possibly with a few lumps on it), reach high amplitude in such striking shapes, and then disappear into the same background again. We reveal that these rogue curves would arise when an internal parameter in bilinear expressions of the rogue waves is real and large. Analytically, we show that these rogue curves are predicted by root curves of certain types of double-real-variable polynomials. We compare analytical predictions of rogue curves to true solutions and demonstrate good agreement between them.
我们报告了在Davey-Stewartson I方程中出现的新的 rogue 波模式，其波峰在空间平面中形成闭合或开放曲线，我们将其称为 rogue 曲线。这些 rogue 曲线呈现出各种引人注目的形状，如环形、双环形等等。它们从均匀背景（可能带有一些隆起）中出现，以如此引人注目的形状达到高振幅，然后再次消失于同一背景中。我们揭示，当 rogue 波的双线性表达式中的一个内部参数为实数且较大时，这些 rogue 曲线就会出现。通过分析，我们表明这些 rogue 曲线由某些类型的双实变量多项式的根曲线预测。我们将 rogue 曲线的解析预测与真实解进行比较，并证明它们之间具有良好的一致性。
