New Optical Soliton Solutions for Coupled Resonant Davey-Stewartson System with Conformable Operator

This paper investigates the novel soliton solutions of the coupled fractional system of the resonant Davey-Stewartson equations. The fractional derivatives are considered in terms of conformable sense. Accordingly, we utilize a complex traveling wave transformation to reduce the proposed system to an integer-order system of ordinary differential equations. The phase portrait and the equilibria of the obtained integer-order ordinary differential system will be studied. Using suitable mathematical assumptions, the new types of bright, singular, and dark soliton solutions are derived and established in view of the hyperbolic, trigonometric, and rational functions of the governing system. To achieve this, illustrative examples of the fractional Davey-Stewartson system are provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of conformable derivatives on behavior of acquired solutions for different fractional orders is also discussed. By comparing the proposed method with the other existing methods, the results show that the execute of this method is concise, simple, and straightforward. The results are useful for obtaining and explaining some new soliton phenomena.

Soliton, Breather-Like and Dark-Soliton-Breather-Like Solutions for the Coupled Long-Wave-Short-Wave System

In this paper, we will obtain the exact $N$-soliton solution of the coupled long-wave-short-wave system via the developed Hirota bilinear method. Through manipulating the relevant parameters, we will construct different types of solutions which include breather-like solutions and dark-soliton-breather-like solutions. Moreover, we will demonstrate that the interactions of two-soliton and two-breather-like solutions are all elastic through asymptotic analysis method. Finally, we will display the interactions through illustrations.PACS 05.45.Yv; 02.30.Ik; 42.81.Dp

Deeper properties of the nonlinear Phi-four and Gross-Pitaevskii equations arising mathematical physics

In this paper, the rational sine–cosine and rational sinh–cosh methods are applied in extracting some properties of nonlinear Phi-four and Gross–Pitaevskii equations. The singular periodic wave solutions, dark soliton solutions and hyperbolic function solutions are reported. The solitary waves are observed from the traveling waves under the values of the parameters. Modulation instability analysis is also observed in various simulations. We also plot to observe the wave distributions of parameters of stability in 2D and 3D visuals via package program.

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.

Sequential generation of self-starting diverse operations in all-fiber laser based on thulium-doped fiber saturable absorber

Self-starting Q-switching, Q-switched mode-locking and mode-locking operation modes are achieved sequentially in an all-fiber erbium-doped fiber laser with thulium-doped fiber saturable absorber for the first time. The central wavelengths of Q-switching, Q-switched mode-locking and mode-locking operation modes are 1569.7 nm, 1570.9 nm, and 1572 nm, respectively. The mode-locking operation of the proposed fiber laser generates stable dark soliton with a repetition rate of 0.99 MHz and signal-to-noise ratio of 65 dB. The results validate the capability of generating soliton pulse by doped fiber saturable absorber. Furthermore, the proposed fiber laser is beneficial to the applications of optical communication and signal processing system.

New Optical Soliton Solutions For The Variable Coefficients Nonlinear Schrodinger Equation

This paper is appropriated to seek new optical soliton solutions of nonlinear Schrodinger equation (NLSE) with time-dependent coefficients which describes the dispersion decreasing fiber. By proposing Bernoulli (G ′/G)-expansion method, where G = G(ζ ) satisfies Bernoulli equation, some periodic wave, bright and dark soliton solutions are successfully achieved. In addition, 3D, line and contour maps graphs of the obtained results under effect of different values of coefficients are illustrated to have acceptable conception of dynamic structures.

The New Solitary Solutions to the Time-Fractional Coupled Jaulent–Miodek Equation

Here, two applicable methods, namely, the tan θ / 2 -expansion technique and modified exp − θ ξ -expansion technique are being applied on the time-fractional coupled Jaulent–Miodek equation. Materials such as photovoltaic-photorefractive, polymer, and organic contain spatial solitons and optical nonlinearities, which can be identified by seeking from energy-dependent Schrödinger potential. Plentiful exact traveling wave solutions containing unknown values are constructed in the sense of trigonometric, hyperbolic, exponential, and rational functions. Different arbitrary constants acquired in the solutions help us to discuss the dynamical behavior of solutions. Moreover, the graphical representation of solutions is shown vigorously in order to visualize the behavior of the solutions acquired for the mentioned equation. We obtain some periodic, dark soliton, and singular-kink wave solutions which have considerably fortified the existing literature on the time-fractional coupled Jaulent–Miodek equation. Via three-dimensional plot, density plot, and two-dimensional plot by utilizing Maple software, the physical properties of these waves are explained very well.

Bright--Dark Solitons in the Space-Shifted Nonlocal Coupled Nonlinear Schrodinger Equation

Multiple bright-dark soliton solutions in terms of determinants for the space-shifted nonlocal coupled nonlinear Schro¨dinger (CNLS) equation are constructed by using the bilinear (Kadomtsev-Petviashvili) KP hierarchy reduction method. It is found that the bright-dark two-soliton only occur elastic collisions. Upon their amplitudes, the bright two solitons only admit one pattern whose amplitude are equal, and the dark two solitons have three different non-degenerated patterns and two different degenerated patterns. The bright-dark four-soliton is the superposition of the two-soliton pairs and can generated bound-state solitons. The multiple double-pole bright-dark soliton solutions are generated through the long wave limit of the obtained bright-dark soliton solutions, and their collision dynamics are also investigated.PACS 02.30.Jr · 03.75.Lm · 04.20.Jb · 05.45.Yv