Optical nondegenerate solitons in a birefringent fiber with a 35 degree elliptical angle.

In this paper, we investigate the optical nondegenerate solitons in a birefringent fiber with a 35 degree elliptical angle. We derive the nondegenerate bright one- and two-soliton solutions by solving the coupled Schrödinger equation. The formation of nondegenerate solitons is related to the wave numbers of the solitons, and we further demonstrate that it is caused by the incoherent addition of different components. We note that the interaction between two degenerate solitons or a nondegenerate soliton and a degenerate soliton is usually inelastic. This is led to the incoherent interaction between solitons of different components and the coherent interaction between solitons of the same component. Through the asymptotic analysis, we find that the two degenerate solitons are elastic interactions under certain conditions, and analyzed the influence of the Kerr nonlinear intensity coefficient γ and the second-order group velocity dispersion ß2 in this system on solitons: the velocity and amplitude of the solitons are proportional to |ß2|, while the amplitude of the solitons is inversely proportional to γ. Two nondegenerate solitons are elastic interactions, but the phase of the soliton can be adjusted to make it inelastic. Furthermore, regardless of the situation mentioned above, total intensities of the solitons before the interaction are equal to that after the soliton interaction.

Periodic and localized waves in parabolic-law media with third- and fourth-order dispersions.

Considering the higher-order nonlinearity is essential in a broad range of real physical media as it significantly influences the wave dynamics in these systems. We study the propagation of femtosecond light pulses inside an optical fiber medium exhibiting higher-order dispersion and cubic-quintic nonlinearities. Pulse evolution in such a system is governed by a higher-order nonlinear Schrödinger equation incorporating second-, third-, and fourth-order dispersions as well as cubic and quintic nonlinearities. The periodic and solitary wave solutions are identified using the equation method. Results presented indicated the potentially rich set of periodic waves in the system under the combined influence of higher-order dispersive effects and cubic-quintic nonlinearity. The velocity of these structures is uniquely dependent on all orders of dispersion. Conditions on the optical fiber parameters for the existence of these exact stable solutions are found by analytical stability analysis.

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..

Propagation of dipole solitons in inhomogeneous highly dispersive optical-fiber media.

We consider ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schrödinger equation with varying second-, third-, and fourth-order dispersions, cubic nonlinearity, and linear gain or loss. We construct a type of exact self-similar soliton solution that takes the structure of a dipole via a similarity transformation connected to the related constant-coefficients one. The conditions on the optical-fiber parameters for the existence of these self-similar structures are also given. The results show that the contribution of all orders of dispersion is an important feature to form this kind of self-similar dipole pulse shape. The dynamic behaviors of the self-similar dipole solitons in a periodic distributed amplification system are analyzed. The significance of the obtained self-similar pulses is also discussed. By performing numerical simulations, the self-similar soliton solutions are found to be stable under slight disturbance of the constraint conditions and the initial perturbation of white noise.

Solitons in the nonlinear Schrödinger equation with two power-law nonlinear terms modulated in time and space.

A nonlinear Schrödinger equation that includes two terms with power-law nonlinearity and external potential modulated both on time and on the spatial coordinates is considered. The model appears in various branches of contemporary physics, especially in the case of lower values of the nonlinearity power. A significant generalization of the similarity transformations approach to construct explicit localized solutions for the model with arbitrary power-law nonlinearities is introduced. We obtain the exact analytical bright and kink soliton solutions of the governing equation for different nonlinearities and potentials that are of particular interest in applications to Bose-Einstein condensates and nonlinear optics. Necessary conditions on the physical parameters for propagating envelope formation are presented. The obtained results can be straightforwardly applied to a large variety of nonlinear Schrödinger models and hence would be of value to understand nonlinear phenomena in a diversity of nonlinear media.