Wang Li, Yan Zhenya, Guo Boling
Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China.
Chaos. 2020 Jan;30(1):013114. doi: 10.1063/1.5129313.
In this paper, we focus on the integrable Hirota equation, which describes the propagation of ultrashort light pulses in optical fibers. First, we numerically study spectral signatures of the spatial Lax pair with distinct potentials [e.g., solitons, Akhmediev-Kuznetsov-Ma (AKM) and Kuznetsov-Ma (KM) breathers, and rogue waves (RWs)] of the Hirota equation. Second, we discuss the RW generation by using the dam-break problem with a decaying initial condition and further analyze spectral signatures of periodized wavetrains. Third, we explore two kinds of noise-derived modulational instabilities: (i) the one case is based on the initial condition (one plus a random noise) such that the KM and AKM breathers, and RWs can be generated, and they agree well with analytical solutions; (ii) another case is to consider another initial condition (one plus a Gaussian wave with a random noise phase) such that some RWs with higher amplitudes can be found. Moreover, we also investigate the spectral signatures of corresponding periodic wavetrains. Finally, we find that the interactions of two waves can also generate the RW phenomena with higher amplitudes. These obtained results will be useful to understand the RW generation in the third-order nonlinear Schrödinger equation and other related models.
