Solitons

Feiyan Liu, Qin Zhou

Abstract We investigate oscillatory soliton pairs including the bright–bright solitons, dark–dark solitons, bright–dark solitons and beating solitons (beating soliton refers to a type of soliton characterized by components that are each composed of both bright and dark solitons, and the overall density is equivalent to that of a single soliton) in the spin-orbit coupled spin-1/2 Bose–Einstein condensates. Two important effects that are the spin orbit coupling (SOC) and Raman detuning resonance on these solitons are studied. The results show that the intensity of SOC affects the spatial oscillation of solitons, while Raman detuning resonance affects the temporal oscillation of solitons. Moreover, the oscillatory soliton pairs and their background are affected by gain/loss. Under different gain/loss modulator, the periodic, parabolic, dromion type and line solitons are constructed for bright–bright pairs, and the periodic and parabolic background planes are presented for dark–dark soliton pairs, as well as the bound state solitons on periodic and kink type background planes are obtained for bright–dark soliton pairs. For one-beating soliton pairs, two types of beating solitons including the petal and breather-like are discovered by adjusting the wave number. For two-beating soliton pairs, the interaction between different combinations of the two types of beating solitons mentioned above, especially the X- and Y-type beating solitons, are presented by controlling two wave numbers. Furthermore, we verify the stability of soliton pairs through numerical simulation and the physics-informed neural network methods.

Carlo F. Barenghi, Thomas Bland, Nick G. Parker

Carlo F. Barenghi, Nick G. Parker

Akira Terai, Yoshiyuki Ono

The dynamics of solitons in spin-density-wave systems is studied numerically using the one-dimensional Hubbard model. The motion of solitons is induced by an electric field, which is introduced into the model in the form of a time-dependent vector potential. The unrestricted Hartree-Fock approximation is used. An improved method of the decomposition of exponential operator is used to solve the time-dependent Hartree-Fock equation. First, the motion of a single soliton is studied, with emphasis on discrete lattice effects. It is found that the discreteness effects reduce the soliton saturation velocity which was found in a previous paper. Second, processes of collisions between a soliton and an antisoliton are studied. The states after the collision are quite different between the cases with a charge soliton pair and with a neutral soliton pair. In the case of the charged soliton pair, the solitons repel each other and reflect to opposite directions. In the case of the neutral soliton pair. In the case of the charged soliton pair, the solitons repel each other and reflect to opposite directions. In the case of the neutral soliton pair, the solitons attract each other to make a dynamical bound state.

Noriaki Horiuchi

Yevgeniya Larionova, Carl O. Weiss

This study reports the characteristics of dark solitons different from bright solitons. A striking feature of dark solitons observed in this work is a reflectivity higher than 1 at the center of the soliton. The reflectivity higher than 1 results because the soliton collects energy from its surrounding. As has been predicted for bright solitons this constitutes an optical amplification mechanism worthwhile considering for technical applications. Results show that in addition to the differential gain predicted for bright solitons, the dark solitons experimentally observed permit "DC gain", i.e. the reflected intensity is higher than the incident intensity. Thus dark solitons show "absolute" gain.