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In this study, we study two generalized stochastic Korteweg-de Vries (KdV) equations. The Painlevé property of these nonlinear models is tested using Kruksal's method, which establishes the model's integrability. As a result, using Hirota's bilinear approach and symbolic computation, the N-soliton solutions are constructed. In addition, the extended hyperbolic function method (EHFM), the modified Kudryashov method (MKM), and the sub-equation method (SEM) are used to acquire the bright soliton, dark soliton, singular soliton, periodic, rational, and exponential solutions. To help understand the dynamic features of the derived soliton solutions, we present a number of 2D, 3D, and contour graphs using appropriate parametric values. [ABSTRACT FROM AUTHOR]

This article studies dark, bright, trigonometric and rational optical soliton solutions to the perturbed nonlinear Schrödinger–Hirota equation (PNLSHE). Hence, we have examined two cases: first, restrictions have been done to the third-order (TOD) (γ) as constraint relation, and the coupling coefficients (σ) is obtained as well as the velocity of the soliton by adopting the traveling wave hypothesis. Second, the TOD and the coupling coefficients are non-zero value, sending back to the PNLSHE, which has been studied in refs. [4,10,16] recently. By employing two relevant integration technics such as the auxiliary equation and the modified auxiliary equation method, miscellaneous optical solitary wave is obtianed, which is in agreement with the outcomes collected by the previous studies [4,16]. These results help in obtaining nonlinear optical fibers in the future.

In this work, shallow ocean-wave soliton, breather, and lump wave solutions, as well as the characteristics of interaction between the soliton and lump wave in a multi-dimensional nonlinear integrable equation with time-variable coefficients, are investigated. The Painlevé analysis is used to verify the integrability of this model. Based on the bilinear form of this model, we use the simplified Hirota's method obtained from the perturbation approach and various auxiliary functions to construct the aforementioned solutions. Besides, the interaction between the soliton and lump wave solutions is also examined. In addition, by imposing specific constraint conditions on the N-soliton solutions, we further derive higher-order breather solutions. To show the physical characteristics of this model, several graphical representations of the discovered solutions are established. These graphs show that the time-variable coefficients result in a variety of novel dynamic behaviors that differ significantly from those for integrable equations with constant coefficients. The acquired results are useful for the study of shallow water waves in fluid dynamics, marine engineering, nonlinear sciences, and ocean physics. [ABSTRACT FROM AUTHOR]

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a recursive Darboux transformation in a generalized form of a focusing vector Nonlinear Schrödinger Equation (NLSE) known as the Manakov System. We apply this generalized recursive Darboux transformation to the Lax-pairs of this system in view of generating the Nth-order vector generalization rogue wave solutions with a rule of iteration. We discuss from first- to three-order vector generalizations of rogue wave solutions while illustrating these features with some 3D, 2D graphical depictions. We illustrate a clear connection between higher-order rogue wave solutions and their free parameters for better understanding the physical phenomena described by the Manakov system [ABSTRACT FROM AUTHOR]

This work addresses the analytical investigation of the prey–predator behavior modeled by nonlinear evolution equation systems with fractional derivative order. Through the New Extended Algebraic Method (NEAM), we unearthed diverse types of soliton solutions including bright, dark solitons, combined trigonometric function solutions, and singular solutions. Besides the results obtained in the work of Khater, some new complex soliton solutions are also unearthed. The NEAM can also be used like the synthesis of the two mathematical tools. [ABSTRACT FROM AUTHOR]

In this paper, we examined the effects of the nonlinear parameters and driven amplitude on the training envelope in discrete cubic-quintic nonlinear Schrödinger equation with arbitrarily high-order nonlinearities. From the numerical simulation, we exhibited the generation of the train of pulses and dark soliton when the driven amplitude is above the threshold. For a specific time of propagation, we illustrate how the variation of the driven amplitude and the nonlinear cubic-quintic parameters can generate instability in the forbidden gap. It emerges that the model of the discrete nonlinear Schrödinger equation with arbitrarily high-order nonlinearities can be used to generate the train of waves despite the fact that it is not integrable in the continuum limit approximation. We also displayed the effects of the cubic-quintic terms on the modulation instability growth rate. The obtained results will open new features to the train of pulses and dark soliton in the nonlinear fibers optics. • We studied discrete cubic-quintic nonlinear Schrödinger equation with arbitrarily high-order nonlinearities. • We examined the effects of the nonlinear parameters and driven amplitude on the training envelope in this nonlinear model. • We illustrated the effects of the cubic-quintic terms on the modulation instability growth rate. • The obtained solutions are depicted by 2D and 3D plots. [ABSTRACT FROM AUTHOR]