聚焦非线性薛定谔方程呼吸子气体的数值谱合成

Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation.

作者信息

Roberti Giacomo, El Gennady, Tovbis Alexander, Copie François, Suret Pierre, Randoux Stéphane

机构信息

Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom.

Department of Mathematics, University of Central Florida, Orlando, Florida 32816, USA.

出版信息

Phys Rev E. 2021 Apr;103(4-1):042205. doi: 10.1103/PhysRevE.103.042205.

DOI:10.1103/PhysRevE.103.042205

PMID:34005925

Abstract

We numerically realize a breather gas for the focusing nonlinear Schrödinger equation. This is done by building a random ensemble of N∼50 breathers via the Darboux transform recursive scheme in high-precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma, and Peregrine breathers as elementary quasiparticles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a "trial" generic (Tajiri-Watanabe) breather and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory [El and Tovbis, Phys. Rev. E 101, 052207 (2020)2470-004510.1103/PhysRevE.101.052207].

摘要

我们通过数值方法实现了聚焦非线性薛定谔方程的呼吸子气体。这是通过在高精度算法中利用达布变换递归方案构建一个包含约50个呼吸子的随机系综来完成的。根据与阿赫梅迪耶夫、库兹涅佐夫-马和佩雷格林呼吸子相对应的三种典型光谱构型，合成了三种类型的呼吸子气体，将其作为各自气体的基本准粒子。通过让一个“试验”通用（田尻-渡边）呼吸子在构建的呼吸子气体中传播，并将平均传播速度与最近发展的光谱动力学理论[埃尔和托夫比斯，《物理评论E》101, 052207 (2020)2470 - 004510.1103/PhysRevE.101.052207]的预测结果进行比较，研究了所构建呼吸子气体的相互作用特性。