Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions

Simulation of universal optical logic gates under energy sharing collisions of Manakov solitons and fulfillment of practical optical logic criteria

The universal optical logic gates, namely, nand and nor gates, have been theoretically simulated by employing the energy sharing collision of bright optical solitons in the Manakov system, governing pulse propagation in a highly birefringent fiber. Further, we also realize the two-input optical logic gates, such as and, or, xor, xnor, for completeness of our scheme. Interestingly, our idea behind the simulation naturally satisfies all the criteria for practical optical logic, which in turn displays the strength and versatility of our theoretical simulation of universal optical logic gates. Hence, our approach paves the way for the experimentalists to create a new avenue in this direction if the energy sharing collisions of Manakov solitons are experimentally realized in the future.

Fundamental and second-order dark soliton solutions of two- and three-component Manakov equations in the defocusing regime

We present exact multiparameter families of soliton solutions for two- and three-component Manakov equations in the defocusing regime. Existence diagrams for such solutions in the space of parameters are presented. Fundamental soliton solutions exist only in finite areas on the plane of parameters. Within these areas, the solutions demonstrate rich spatiotemporal dynamics. The complexity increases in the case of three-component solutions. The fundamental solutions are dark solitons with complex oscillating patterns in the individual wave components. At the boundaries of existence, the solutions are transformed into plain (nonoscillating) vector dark solitons. The superposition of two dark solitons in the solution adds more frequencies in the patterns of oscillating dynamics. These solutions admit degeneracy when the eigenvalues of fundamental solitons in the superposition coincide.

Interaction dynamics of optical dark bound solitons for a defocusing Lakshmanan-Porsezian-Daniel equation

We investigate the propagation and interaction dynamics of the optical dark bound solitons for the defocusing Lakshmanan-Porsezian-Daniel equation, which is a physically relevant generalization of the nonlinear Schrödinger equation involving the higher-order effects. Explicit N-dark soliton solutions in the compact determinant form are constructed via the binary Darboux transformation method. Bound states of the dark solitons are discussed when the incoherent solitons have the same velocity. We find an interesting phenomenon that dark soliton molecules and double-valley dark solitons (DVDSs) can be obtained by controlling the interval of the bound state dark solitons, and abundant interaction modalities between them can be formed. Moreover, dark soliton molecules always undergo elastic interactions with other solitons, while interactions for the DVDSs are usually inelastic, and special parameter conditions for elastic interaction of DVDSs through asymptotic analysis are obtained. Numerical simulations are employed to verify the stability of the bound state dark solitons. Analytical results obtained in this paper are expected to be useful for the experimental realization of bound-state dark solitons in optical fibers with higher-order effects and a further understanding of their optical transmission properties..

Some anomalous exact solutions for the four-component coupled nonlinear Schrödinger equations on complex wave backgrounds

The coupled nonlinear Schrödinger (CNLS) equations are the important models for the study of the multicomponent Bose-Einstein condensates (BECs). In this paper, we study the four-components CNLS equations via Darboux transformation and obtain the N-soliton solutions with zero seed and non-zero seed solutions([Formula: see text] or [Formula: see text]. The 1-soliton solution and 2-soliton solution are calculated on complex wave backgrounds, the dark-bright-bright-bright soliton solutions and dark-dark-bright-bright soliton solutions are constructed. We can obtain a new class of dark-bright-bright-bright soliton solutions, which admit one-valley dark soliton in component [Formula: see text] and triple-hump bright solitons in the other three components. The collision properties between dark-dark-bright-bright solitons are considered, and the vector solitons are expected to be much more abundant than those of previously reported vector soliton collisions.

Phase characters of optical dark solitons with third-order dispersion and delayed nonlinear response

Dark soliton is usually seen as one of the simplest topological solitons, due to phase shift across its intensity dip. We investigate phase characters of single-valley dark soliton (SVDS) and double-valley dark soliton (DVDS) in a single-mode optical fiber with third-order dispersion and delayed nonlinear response. Notably, two different phase shifts can produce an SVDS with the same velocity under some conditions, which is not admitted for a dark soliton with only the second-order dispersion and self-phase modulation, whose phase shift and velocity is a one-to-one match. This phase property of SVDS can be used to explain the generation of previously reported DVDS in Hirota equation and make DVDSs show two types of phase profiles. Moreover, the different topological vector potentials underlying the distinct phase profiles have been uncovered. We further explore the collision properties of the DVDSs by analyzing their topological phases. Strikingly, the inelastic collision can lead to the conversion between the two types of phase profiles for DVDS. The results reveal that inelastic or elastic collision can be judged by analyzing virtual topological magnetic fields.

Dynamics of nondegenerate vector solitons in a long-wave-short-wave resonance interaction system

In this paper, we study the dynamics of an interesting class of vector solitons in the long-wave-short-wave resonance interaction (LSRI) system. The model that we consider here describes the nonlinear interaction of long wave and two short waves and it generically appears in several physical settings. To derive this class of nondegenerate vector soliton solutions we adopt the Hirota bilinear method with the more general form of admissible seed solutions with nonidentical distinct propagation constants. We express the resultant fundamental as well as multisoliton solutions in a compact way using Gram-determinants. The general fundamental vector soliton solution possesses several interesting properties. For instance, the double-hump or a single-hump profile structure including a special flattop profile form results in when the soliton propagates in all the components with identical velocities. Interestingly, in the case of nonidentical velocities, the soliton number is increased to two in the long-wave component, while a single-humped soliton propagates in the two short-wave components. We establish through a detailed analysis that the nondegenerate multisolitons in contrast to the already known vector solitons (with identical wave numbers) can undergo three types of elastic collision scenarios: (i) shape-preserving, (ii) shape-altering, and (iii) a shape-changing collision, depending on the choice of the soliton parameters. Here, by shape-altering we mean that the structure of the nondegenerate soliton gets modified slightly during the collision process, whereas if the changes occur appreciably then we call such a collision as shape-changing collision. We distinguish each of the collision scenarios, by deriving a zero phase shift criterion with the help of phase constants. Very importantly, the shape-changing behavior of the nondegenerate vector solitons is observed in the long-wave mode also, along with corresponding changes in the short-wave modes, and this nonlinear phenomenon has not been observed in the already known vector solitons. In addition, we point out the coexistence of nondegenerate and degenerate solitons simultaneously along with the associated physical consequences. We also indicate the physical realizations of these general vector solitons in nonlinear optics, hydrodynamics, and Bose-Einstein condensates. Our results are generic and they will be useful in these physical systems and other closely related systems including plasma physics when the long-wave-short-wave resonance interaction is taken into account.