A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains in the quasi one-dimensional confinement is shown. Additionally, fragmentation of a BEC has been observed outside confinement, in free space. In the end a double BEC production setup for studying soliton collisions is described. PACS numbers: 03.75.Lm, 67.85.Hj I. INTRODUCTION Non-dispersing wavepackets called solitons appear in many non-linear physical systems. Examples of solitons can be found in water waves [1], acoustic waves [2], light propagating through non-linear materials [3], plasmas [4], energy propagation along proteins [5], and many other systems including Bose-Einstein condensates (BECs) of cold atoms. Experimental research on solitons in BECs began with creation of a dark soliton [6, 7], followed by a bright soliton [8] and bright soliton trains [9]. Observation of more exotic gap solitons [10], decay of dark solitons into vortex rings [11], interactions between solitons [12-14], their interactions with impurities [15], optical potential barriers [16], speckle potentials [17] and demonstration of a matter-wave interferometer [18] show that a cold-atom BEC is an excellent and versatile system for studying solitons.Formation of solitons in a BEC depends on the twobody interaction between the atoms and the geometry of the trap used to confine the BEC. A quasi-onedimensional (quasi-1D) confinement is needed, which can be achieved in either magnetic or optical dipole traps. In such traps a dark soliton forms as a trough of lower density within a BEC with repulsive interatomic interaction while a bright soliton is a wavepacket comprising the whole BEC with attractive interatomic interaction that can move over macroscopic distances in a vacuum. So-called dark-bright solitons can be supported in twocomponent BECs, where atoms with one spin component fill the dark soliton within the BEC of the other spin component [13,19,20].Usually, only unchanging waves in one-dimensional integrable systems are called solitons. In quasi-1D harmonically confined geometry integrability is broken, but only slightly so. The solitary waves that form from BECs are three-dimensional objects, not one-dimensional, but their propagation is limited to one-dimension. The name soliton in this paper is used in its broader meaning com-

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Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

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