Soliton Solutions and Collisions for the Multicomponent Gross–Pitaevskii Equation in Spinor Bose–Einstein Condensates

In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an F=2 spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain the explicit bright one- and two-soliton solutions for the equation via symbolic computation. With the choice of polarization parameter and spin density, the one-soliton solutions are divided into four types: one-peak solitons in the ferromagnetic and cyclic states and one- and two-peak solitons in the polar states. For the former two, solitons share the similar shape of one peak in all components. Solitons in the polar states have the one- or two-peak profiles, and the separated distance between two peaks is inversely proportional to the value of polarization parameter. Based on the asymptotic analysis, we analyze the collisions between two solitons in the same and different states.

ULF Pre-Seismic Geomagnetic Anomalous Signal Related to Mw8.1 Offshore Chiapas Earthquake, Mexico on 8 September 2017

In the last decade, the real time ground–based geomagnetic observations realized in correlation with the Vrancea seismicity in Romania, together with supplementary studies related to some earthquakes (Mw9.0 Tohoku, Japan on 11 March 2011 and Mw8.3 Coquimbo, Chile on 16 September 2015), enlarged our knowledge about the relationship between the pre-seismic anomalous phenomena and the final stage of the earthquake nucleation. To identify possible ultra-low-frequency (ULF) geomagnetic signals prior to the onset of an Mw8.1 earthquake, we retroactively analyzed the data collected on the interval 1 August–16 September 2017 at the Geomagnetic Observatories in Teoloyucan (TEO), Mexico and Tucson (TUC) USA, with the last taken as a reference. Daily mean distributions of the polarization parameter BPOL (geomagnetic polarization parameter) and standard deviation are obtained for both observatories using a fast Fourier transform (FFT) band-pass filtering in the ULF range (0.001–0.083 Hz). Further on, we investigated the singularity of the pre-seismic signal associated with an Mw8.1 earthquake and applied a statistical analysis based on a standardized random variable equation; results are presented as BPOL* time series on the interval 1–26 September. Finally, the hourly mean distribution, obtained as difference BPOL (TUC-TEO) on the interval 7–9 September emphasizes an anomalous signal with five hours before the onset of the Mw8.1 earthquake.