Open AccessCollapse and evolution of wave field based on a generalized nonlinear Schrdinger equation
Author(s) -
Cui Shao-Yan,
Xinxin Li,
Jie Xiao
Publication year - 2016
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.65.040201
Subject(s) - physics , modulational instability , wavelength , instability , nonlinear system , cascade , nonlinear schrödinger equation , field (mathematics) , energy cascade , wavenumber , turbulence , quantum electrodynamics , wave equation , rogue wave , classical mechanics , quantum mechanics , mechanics , mathematics , pure mathematics , chemistry , chromatography
A generalized nonlinear Schrdinger equation is numerically studied using the split-step Fourier method. For a fixed external potential field and an initial pulse disturbance, the effects of the complex coefficients p and q in the nonlinear Schrdinger equation on the evolution of the wave field are investigated. From a large number of simulations, it is found that the evolution of the wave field remains similar for different signs of the real parts of p and q, and different values of the real part of p. The initial pulse consisting of the longest wavelength modes (in the smallest-|k| corner of the phase space) of the spectrum first suffers modulational instability. Collapse begins at t0.1, followed by inverse cascade of the shortest wavelength modes to longer wavelength ones, so that the whole k space becomes turbulent. For p = 1+0.04i, and q = 1+0.6i, it is found that first modulational instability occurs in the longer wavelength regime and the wave energy is transferred to the larger |k| modes. Then the wave collapse appears with increasing wave energy. Next, the large-|k| modes condense into a smaller-|k| mode by inverse cascade before spreading to the center of the phase space, until a turbulent state occurs there. Finally, most of the wave energy is condensed to the neighborhoods of three modes.