Generation and nonlinear dynamics of X waves of the Schrödinger equation

Abstract

The generation of finite energy packets of X-waves is analysed in normally dispersive cubic media by using an X-wave expansion. The 3D nonlinear Schroedinger model is reduced to a 1D equation with anomalous dispersion. Pulse splitting and beam replenishment as observed in experiments with water and Kerr media are explained in terms of a higher order breathing soliton. The results presented also hold in periodic media and Bose-condensed gases.

A Universal Asymptotic Regime in the Hyperbolic Nonlinear Schrödinger Equation

“…the numerical curves in figs. [15][16][17][18][19][20]. The average amplitude and phase are consistent with the corresponding values without noise.…”

“…infinite L 2 -norm |Φ| 2 dxdy), their finite-energy counterparts have been observed in experiments on electromagnetic beam propagation; they appear in the central cores of the beams and split at sufficiently large propagation distance Z, see e.g. [15,16]. When the phenomenon is described by the HNLS equation [12], the end result of their splitting must be the hyperbolic structure which we observe numerically and describe analytically below.…”

“…This is similar to X-wave phenomena cf. [15,16,30] which exhibit characteristic X-shapes in the (x, y)plane formed by the lines x = ±y and characteristic hyperbolas asymptotic to these lines. While such existing exact solutions have infinite energy (i.e.…”

Ultrabroadband Dispersive Radiation by Spatiotemporal Oscillation of Multimode Waves

“…In this regime, promising results have been obtained considering conical waves, which are the eigenmodes of the 3D linear wave equation [5,6]. Conical wave solutions to the nonlinear wave equation may provide deeper insight [7,8]. Given the advantages the concepts of solitons and collapse have provided for studying single-mode waveguides and free space filamentation, it is natural to seek similar concepts in multimode waveguides.…”

Multimodal unidirectional pulse propagation equation

“…B. Propagation example: Fishwave formation in multimode step-index optical fibers close to the zero-dispersion wavelength Few years ago, a strong interest has been devoted to the study of conical waves formation in dispersive nonlinear bulk media [13][14][15][16]. Such waves are particular solutions of the propagation equation in bulk media with the notable feature of being stationary, i.e.…”