Numerical study of highly dispersive optical solitons with differential group delay having quadratic-cubic law of refractive index by Laplace–Adomian decomposition

This paper carries out numerical simulations of highly dispersive optical solitons with differential group delay having quadratic-cubic law of nonlinearity. The Laplace–Adomian decomposition scheme is implemented to visualize the soliton propagation dynamics. Both bright and dark solitons are addressed. The error measure for these numerical approximations is impressively low as presented.

Quantum Dark Solitons in the 1D Bose Gas: From Single to Double Dark-Solitons

We study quantum double dark-solitons, which give pairs of notches in the density profiles, by constructing corresponding quantum states in the Lieb–Liniger model for the one-dimensional Bose gas. Here, we expect that the Gross–Pitaevskii (GP) equation should play a central role in the long distance mean-field behavior of the 1D Bose gas. We first introduce novel quantum states of a single dark soliton with a nonzero winding number. We show them by exactly evaluating not only the density profile but also the profiles of the square amplitude and phase of the matrix element of the field operator between the N-particle and (N−1)-particle states. For elliptic double dark-solitons, the density and phase profiles of the corresponding states almost perfectly agree with those of the classical solutions, respectively, in the weak coupling regime. We then show that the scheme of the mean-field product state is quite effective for the quantum states of double dark solitons. Assigning the ideal Gaussian weights to a sum of the excited states with two particle-hole excitations, we obtain double dark-solitons of distinct narrow notches with different depths. We suggest that the mean-field product state should be well approximated by the ideal Gaussian weighted sum of the low excited states with a pair of particle-hole excitations. The results of double dark-solitons should be fundamental and useful for constructing quantum multiple dark-solitons.

Dark soliton solutions of the cubic-quintic complex Ginzburg–Landau equation with high-order terms and potential barriers in normal-dispersion fiber lasers

In this paper, we numerically study dark solitons in normal-dispersion optical fibers described by the cubic-quintic complex Ginzburg–Landau equation. The effects of the third-order dispersion, self-steepening, stimulated Raman dispersion, and external potentials are also considered. The existence, chaotic content and interactions of these objects are analyzed, as well as the tunneling through a potential barrier and the formation of dark breathers aside from dark solitons in two dimensions and their mutual interactions as well as with periodic potentials. Furthermore, the homogeneous solutions of the model and the conditions for their stability are also analytically obtained.

New Explicit and Exact Traveling Waves Solutions To The Modified Complex Ginzburg Landau Equation

This paper applies function transformation method to obtain under certain conditions bright, dark, kink and W-shaped dark solitons waves solutions to the modified complex Ginzburg Landau Equation (CGLE). These new obtained solutions can be useful in many applications such as communication, medicine, hydrodynamic, thermodynamic just to name a few and can allow to explain physical phenomena.

Novel soliton solutions of four sets of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili-like equations

In this paper, we examined four different forms of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili (B-KP)-like equations. In this connection, an accurate computational method based on the Riccati equation called sub-equation method and its Bäcklund transformation is employed. Using this method, numerous exact solutions that do not exist in the literature have been obtained in the form of trigonometric, hyperbolic, and rational. These solutions are of considerable importance in applied sciences, coastal, and ocean engineering, where the B–KP-like equations modeled for some significant physical phenomenon. The graph of the bright and dark solitons is presented in order to demonstrate the influence of different physical parameters on the solutions. All of the findings prove the stability, effectiveness, and accuracy of the proposed method.

A Novel Dynamic of Localized Solitary Waves for the Hirota-Maccari System

This paper investigates a particular family of semi-rational solutions in determinant form by using the KP hierarchy reduction method, which describe resonant collisions among lumps or resemble line rogue waves and dark solitons in the Hirota-Maccari system. Due to the resonant collisions, the line resemble rogue waves are generated and attenuated in the background of dark solitons with line profiles of finite length, it takes a short time for the lumps to appear from and disappear into the dark solitons background. These novel dynamic of localized solitary waves may be help to understand some physical phenomena of nonlinear localized waves propagation in many physical settings.