The book chapter titled “Dipole Solitons in a Nonlocal Nonlinear Medium with Self-Focusing and Self-Defocusing Quintic Nonlinear Responses” was published in “IntechOpen” by ITU Department of Mathematics Engineering members Res. Asst. Melis Turgut, Prof. Dr. Nalan Antar, and Prof. Dr. İlkay Bakırtaş.


In recent years, dipole solitons have attracted considerable interest because of their unique features and potential applications in nonlinear optics and Bose-Einstein condensates. In this study, the existence and nonlinear stability dynamics of dipole solitons have been investigated for a nonlocal nonlinear medium with the quintic nonlinear response. This medium is characterized by the (2+1)D NLSM system with a periodic external lattice. Dipole solitons are obtained by the squared-operator method, and the nonlinear stability dynamics of these dipole solitons are investigated by their direct simulations. They have demonstrated that solitons can stay nonlinearly stable for a wide range of each parameter, and two nonlinearly stable regions have been found for dipole solitons in the gap domain. Moreover, it is found that the stability of dipole solitons can be improved and the instability that has been observed in some cases can be suppressed by the modification of the potential depth and with a stronger anisotropy coefficient.