Abstract
We study the influence of space-time focusing (STF) on spatiotemporal instability (STI) in nonlinear dispersive media using a modified (3 + 1)-dimensional nonlinear Schrödinger equation (NLSE). We find that, for both normal and anomalous group-velocity dispersions (GVD), STF exerts no influence on the maximum gain of instability spectra, yet alters the instability regions fundamentally. In the normal GVD case, STF significantly shrinks the instability region by suppressing the growth of the higher frequency components; while in the anomalous GVD case, it slightly shrinks the original instability region obtained from the standard (3 + 1)-dimensional NLSE. Most importantly, in both cases, STF may lead to the appearance of new instability regions. Expressions for temporal frequency widths for new instability regions dependent on spatial frequency and STF parameter are obtained. In addition, we find that, the main role played by self-steepening (SS) in STI is that it reduces the instability gain and, comparatively, it exerts much more influence on the new instability region resulted from STF.
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