Abstract
We present the results of numerical and analytical analysis of solutions of the three-dimensional (3D) nonlinear Schröodinger equation with hyperbolic spatial operator. Evolution of the system is considered in separate for two types of the initial field: a Gaussian distribution and a hollow-type (tubular or horseshoe) distribution. The effect of the nonlinear dispersion on wave-packet splitting during self-compression toward the system axis is studied. It is shown that additional focusing of Gaussian wave packets takes place in a wide range of the nonlinear-dispersion parameter. This effect results in a noticeable amplitude growth of one of the two secondary pulses formed as a result of the splitting. For hollow-type distributions, we note the formation of moving inhomogeneities and the excitation of secondary wave fields typical of the hyperbolic system.
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Zharova, N.A., Litvak, A.G. & Mironov, V.A. Self-Action of a Supershort Laser Pulse in a Medium with Normal Group-Velocity Dispersion. Radiophysics and Quantum Electronics 46, 297–306 (2003). https://doi.org/10.1023/A:1026310214469
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DOI: https://doi.org/10.1023/A:1026310214469