Dark solitons in cigar-shaped Bose-Einstein condensates (BECs) of $^{87}$Rb are created using a phase imprinting method. The study reports on the experimental investigation of dark solitons in dilute vapor of $^{87}$Rb. Dark solitons are characterized by a local density minimum and a sharp phase gradient. They are dynamically stable in cigar-shaped traps with strong radial confinement. The dark soliton wavefunction is described by a specific mathematical expression involving the correlation length and speed of sound. The experiment involves applying a phase imprinting potential to one half of the condensate wavefunction, resulting in a dark soliton. The dark soliton moves with a velocity smaller than the speed of sound and is observed to have a density minimum. The velocity of the dark soliton depends on the applied phase shift and the width of the potential edge. The study also shows that dark solitons exhibit thermodynamic and dynamical instabilities in 3D at finite temperatures. However, in 1D, dark solitons are stable. The results are compared with numerical simulations of the 3D Gross-Pitaevskii equation, showing good agreement. The dark soliton velocity decreases with increasing phase shift and is influenced by the width of the potential edge. The experiment demonstrates that dark solitons can be created and studied in BECs. The results show that dark solitons move with velocities smaller than the speed of sound and are stable in certain conditions. The study also highlights the importance of dissipation in the dynamics of dark solitons, as the soliton contrast decreases over time due to energy loss. The findings suggest that the study of dark solitons in BECs can provide insights into nonlinear phenomena in dissipative environments. The research opens new directions in atomic physics, particularly in understanding the behavior of soliton structures in BECs. The study also discusses potential future experiments, such as creating dark solitons in elongated dipole traps and studying their dynamics with spin as an additional degree of freedom.Dark solitons in cigar-shaped Bose-Einstein condensates (BECs) of $^{87}$Rb are created using a phase imprinting method. The study reports on the experimental investigation of dark solitons in dilute vapor of $^{87}$Rb. Dark solitons are characterized by a local density minimum and a sharp phase gradient. They are dynamically stable in cigar-shaped traps with strong radial confinement. The dark soliton wavefunction is described by a specific mathematical expression involving the correlation length and speed of sound. The experiment involves applying a phase imprinting potential to one half of the condensate wavefunction, resulting in a dark soliton. The dark soliton moves with a velocity smaller than the speed of sound and is observed to have a density minimum. The velocity of the dark soliton depends on the applied phase shift and the width of the potential edge. The study also shows that dark solitons exhibit thermodynamic and dynamical instabilities in 3D at finite temperatures. However, in 1D, dark solitons are stable. The results are compared with numerical simulations of the 3D Gross-Pitaevskii equation, showing good agreement. The dark soliton velocity decreases with increasing phase shift and is influenced by the width of the potential edge. The experiment demonstrates that dark solitons can be created and studied in BECs. The results show that dark solitons move with velocities smaller than the speed of sound and are stable in certain conditions. The study also highlights the importance of dissipation in the dynamics of dark solitons, as the soliton contrast decreases over time due to energy loss. The findings suggest that the study of dark solitons in BECs can provide insights into nonlinear phenomena in dissipative environments. The research opens new directions in atomic physics, particularly in understanding the behavior of soliton structures in BECs. The study also discusses potential future experiments, such as creating dark solitons in elongated dipole traps and studying their dynamics with spin as an additional degree of freedom.