Multipole solitons in a cold atomic gas with a parity-time symmetric potential

Diversiform propagation of hollow Gaussian beam clusters in non-linear media with self-induced parabolic potentials

“…We define Ω j (τ ) as the rotating angle of each component HGB, and the expression of the rotating angle includes the initial azimuth angle φ j of each component beam. The angular velocity of each component HGB is defined as the first derivative of equation (32) and it takes the form as…”

“…When a beam propagates in a non-linear medium, the propagation state of solitons or breathers can be formed because its linear diffraction nature is completely or partially balanced by the non-linear self-focusing effect provided by the medium [15,16]. The propagation characteristics of solitons and breathers have been studied extensively, from theory to experiment, in recent years [31][32][33]. In 2003, hollow Gaussian beam (HGB) is proposed as an important mathematical model to describe dark-hollow beams [34], which has potential applications in atom guiding and trapping [35][36][37][38][39].…”

Exceptional Points in Non-Hermitian Photonic Crystals Incorporated With a Defect

“…In recent years, complex photonic crystals (PCs) have provided a new opportunity to explore the non-Hermitian optical properties and other nonlinearities theoretically and experimentally [22][23][24][25][26][27][28]. Many significant optical characteristics have been discovered in PCs, such as solitons [29][30][31][32][33], topological modes [34,35], and strong absorptions [36][37][38][39]. Furthermore, there are bandgap structures in the transmission spectra as light impinges upon PCs, and light field localization can also be implemented in defective PCs, which could be utilized for enhancing the nonlinearity of materials [40,41] and the lateral shifts of reflected beams [42][43][44][45].…”

Investigation of Interaction Solutions for Modified Korteweg‐de Vries Equation by Consistent Riccati Expansion Method

“…Milan et al found exact fundamental soliton solutions in the spiraling guiding structures by the modified Petviashvilis iteration method [9]. Cheng et al investigated the formation and propagation of a multipole soliton in a cold atomic gas with a parity-time symmetric potential using the modified square operator method [10]. Liu et al obtained the three-soliton solutions for high-order nonlinear Schrodinger equation by Hirotas bilinear method [11].…”