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We will study the transmission of double-hump solitons of the coupled Manakov equations (CME) that have unlimited position for the generation and amplification of double-hump solitons in fiber lasers. These double-hump soliton solutions of CME will be extracted by using three ansatz techniques that are prepared for this target. The first one has profile name the solitary wave ansatz method (SWAM), while the second one has profile name the extended simple equation method (ESEM) and the third one has profile name the Paul-Painlevé approach method (PPAM). The three proposed methods are used for the first time to construct the soliton solutions of this model. The simulation for the 2D, 3D Figures for all obtained solutions has been established. [ABSTRACT FROM AUTHOR]

The main purpose of this study was to produce abundant new types of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation that represents unstable optical solitons that emerge from optical propagations through the use of birefringent fibers. These new types of soliton solutions have behaviors that are bright, dark, W-shaped, M-shaped, periodic trigonometric, and hyperbolic and were not realized before by any other method. These new forms have been detected by using four different techniques, which are, the extended simple equation method, the Paul-Painlevé approach method, the Ricatti-Bernoulli-sub ODE, and the solitary wave ansatz method. These new solitons will be arranged to create a soliton catalog with new impressive behaviors and they will contribute to future studies not only for this model but also for the optical propagations through birefringent fiber.

The main purpose of this study was to produce abundant new types of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation that represents unstable optical solitons that emerge from optical propagations through the use of birefringent fibers. These new types of soliton solutions have behaviors that are bright, dark, W-shaped, M-shaped, periodic trigonometric, and hyperbolic and were not realized before by any other method. These new forms have been detected by using four different techniques, which are, the extended simple equation method, the Paul-Painlevé approach method, the Ricatti-Bernoulli-sub ODE, and the solitary wave ansatz method. These new solitons will be arranged to create a soliton catalog with new impressive behaviors and they will contribute to future studies not only for this model but also for the optical propagations through birefringent fiber. [ABSTRACT FROM AUTHOR]

In this paper, we take into consideration a general form of the extended Kadomtsev–Petviashvili equation, which has several applications in applied sciences and engineering. The Painlevé analysis via WTC–Kruskal algorithm is first used to validate the integrability of this nonlinear model. Thereafter, we determine the multi-solitons, breather solutions, lump waves, rouge waves, lump with solitary waves interaction, and breather with solitons interaction by using various ansatz's functions based on bilinear formalism and symbolic computation. The solitary wave ansatz method is used to extract the bight solitons, dark solitons, singular solitons, and the periodic function solutions. In addition, the Ma-breather, Kuznetsov–Ma breather, and their associated rogue wave solutions are also discussed. In order to demonstrate several physical structures, the figures relating to these solutions are illustrated by selecting appropriate parametric values in 2D, 3D, and contour plots with the assistance of the symbolic package Mathematica 13.1. The dynamics of nonlinear wave models are addressed by these solutions. [ABSTRACT FROM AUTHOR]

Using the well-known solitary wave ansatz method, we obtain new exact bright and dark soliton solutions for two nonlinear Schrö dinger equations, namely, the perturbed nonlinear Schrö dinger equation with the Kerr law nonlinearity and a higher order nonlinear Schrö dinger equation which describe the propagation of ultra short pulses in nonlinear optical fibers. The parameters of the soliton envelope (amplitude, width, velocity) are obtained as a function of the dependent model coefficients. Comparing the new solutions for these two equations with the well-known results are given. [ABSTRACT FROM AUTHOR]

The Schäfer-Wayne short-pulse equation, which governs the propagation of ultra-short light pulses in silica optical fibres is analytically investigated. The sine-cosine method and solitary wave ansatz method are used for a reliable treatment of short-pulse equation. It should be noted that the study of this model admitting soliton-type solutions is very useful for future research work. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new exact solutions of compound KdV-Burgers system with nonlinear terms of any order by using the $$(\frac{G^{\prime }}{G})$$-expand method. In addition, the solitary wave ansatz method is used to carry out this integration. Subsequently, it has been proved that the soliton solution exist only for the KdV-Burgers equation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the Klein–Gordon–Zakharov equations which model the interaction between the Langmuir wave and the ion acoustic wave in a high frequency plasma, are considered. To examine the role played by the nonlinear dispersion term in the formation of solitons, a family of the considered equations with power law nonlinearity are investigated. By using two solitary wave ansatze in terms of and functions, we find exact analytical bright and dark soliton solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The conditions of existence of solitons are presented. These closed form solutions are helpful to well understand the mechanism of the complicated physical phenomena and dynamical processes modeled by the used model. [Copyright &y& Elsevier]

Abstract: We consider a nonlinear dispersive Zakharov–Kuznetsov (for short, ) equation. This equation governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. A special form of this model with time-dependent coefficients of the nonlinear terms as well as the nonlinear dispersion terms is studied. Further, there are time-dependent linear attenuation and generalized evolution terms. The solitary wave ansatz is used to carry out the integration and an exact one-soliton solution is obtained. The parameters of the soliton envelope (amplitude, widths, velocity) are explicitly calculated in the course of the derivation of the exact solution, as functions of the varying model coefficients. The constraint relation between these time-dependent coefficients for the one-soliton solution to exist is established. [Copyright &y& Elsevier]

Different types of soliton wave solutions for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq equations are investigated via the solitary wave ansatz method. These solutions are classified into three categories, namely solitary wave, shock wave, and singular wave solutions. The corresponding integrability criteria, termed as constraint conditions, obviously arise from the study. Moreover, the influences of the free parameters and interaction properties in these solutions are discussed graphically for physical interests and possible applications. [ABSTRACT FROM AUTHOR]