Two-dimensional self-similarity transformation theory and line rogue waves excitation

Jie-Fang Zhang,Ding-Guo Yu,Mei-Zhen Jin

doi:10.7498/aps.71.20211417

Abstract

A two-dimensional self-similarity transformation theory is established, and the focusing (parabolic) (2 + 1)-dimensional NLS equation is taken as the model. The two-dimensional self-similarity transformation is proposed for converting the focusing (2 + 1)-dimensional NLS equation into the focusing (1 + 1) dimensional NLS equations, and the excitation of its novel line-rogue waves is further investigated. It is found that the spatial coherent structures induced by the Akhmediev breathers (AB) and Kuznetsov-Ma solitons (KMS) also have the short-lived characteristics which are possessed by the line-rogue waves induced by the Peregrine solitons, and the other higher-order rogue waves and the multi-rogue waves of the (1 + 1) dimensional NLS equations. This is completely different from the evolution characteristics of spatially coherent structures induced by bright solitons (including multi-solitons and lump solutions), with their shapes and amplitudes kept unchanged. The diagram shows the evolution characteristics of all kinds of resulting line rogue waves. The new excitation mechanism of line rogue waves revealed contributes to the new understanding of the coherent structure of high-dimensional nonlinear wave models.

Highlights

2 + 1)dimensional NLS equation is taken as the model
It is found that the spatial coherent structures induced by the
the short-lived characteristics which are possessed by the line-rogue waves induced by the

Summary

PS 诱导的线怪波

图 1 展示了 (2 + 1) 维 NLS 方程 (1) 的一阶线怪波 (2) 随传播变量 t 的演化图, 图中的自由参数选为 λ = 1, γ = 2, κ0 = ι0 = −a0 = b0 = 1. 图 1 一阶单线怪波 (28) 在 (x, y)-平面上随t的演化图 : (a) t = −3 ; (b) t = 0 ; (c) t = 5 , 自由参数选取为α = β = λ = 1, γ = 2, κ0 = ι0 = −a0 = b0 = 1. 图 2 二阶单线怪波 (29) 在 (x, y)-平面上随t的演化图 : (a) t = −3 ; (b) t = 0 ; (c) t = 5 , 自由参数选取为α = β = λ = 1, γ = 2, κ0 = ι0 = −a0 = b0 = 1 , ξd = τd = 0 Fig. 2. 至于 (2 + 1) 维 NLS 方程 (10) 的更高阶怪波, 可. 至于 (2 + 1) 维 NLS 方程 (10) 的其他形态的怪波簇诱导的多线怪波, 可以类似讨论, 限于篇幅从略线怪波. 至于 (2 + 1) 维 NLS 方程 (10) 的其他形态的怪波簇诱导的多线怪波, 可以类似讨论, 限于篇幅从略

AB 诱导的多线怪波

KMS 诱导的单线怪波