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Nonlinear Schrödinger equations are a key paradigm in nonlinear research, attracting both mathematical and physical attention. This work was primarily concerned with the usage of a reliable analytic technique in order to solve two models of (2+1)-dimensional nonlinear Schrödinger equations. By applying a comprehensible wave transformation, every nonlinear model was simplified to an ordinary differential equation. A number of critical solutions were observed that correlated to various parameters. The provided approach has various advantages, including reducing difficult computations and succinctly presenting key results. Some 2D and 3D graphical representations regarding presented solitons were considered for the appropriate values of the parameters. We also showed the effect of the physical parameters on the dynamical behavior of the presented solutions. Finally, the proposed approach may be expanded to tackle increasingly complicated problems in applied science. [ABSTRACT FROM AUTHOR]

The shear shallow water (SSW) model introduces an approximation for shallow water flows by including the effect of vertical shear in the system. Six non-linear hyperbolic partial differential equations with non-conservative laws make up this system. Shear, contact, rarefaction, and shock waves are all admissible in this model. We developed the finite-volume two-step scheme, the so-called generalized Rusanov (G. Rusanov) scheme, for solving the SSW model. This method is split into two stages. The first one relies on a local parameter that permits control over the diffusion. In stage two, the conservation equation is recovered. Numerous numerical instances were taken into consideration. We clarified that the G. Rusanov scheme satisfied the C-property. We also compared the numerical solutions with those obtained from the Rusanov, Lax-Friedrichs, and reference solutions. Finally, the G. Rusanov technique may be applied for solving a wide range of additional models in developed physics and applied science. [ABSTRACT FROM AUTHOR]

In this work, we consider the model of shallow water equation with horizontal density gradients. We develop the modified Rusanov (mR) scheme to solve this model in one and two dimensions. Predictor and corrector are the two stages of the suggested scheme. The predictor stage is dependent on a local parameter (αn i+1/2) that allows for difiusion control. The balance conservation equation is recovered in the corrector stage. The proposed approach is well-balanced, conservative, and straightforward. Several 1D and 2D test cases are produced after presenting the shallow water model and the numerical technique. In the 1D case, we compared the proposed scheme with the Rusanov scheme, mR with constant and analytical solutions. The numerical simulation demonstrates the mR's great resolution and attests to its capacity to produce accurate simulations of the shallow water equation with horizontal density gradients. Our results demonstrate that the mR technique is a highly effective instrument for solving a variety of equations in applied science and developed physics. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonlinear Chiral Schrödinger equation (CNLSE) in two dimensions where noise term affected randomly with time. This equation characterized some edges states of fractional-Hall Effect features in quantum. The CNLSE with multiplicative noise effects is studied as dynamical system to specify the acceptable solution types and then solved by unified solver method. The presented solutions are periodic envelopes, explosive, dissipative, symmetric solitons, and blow up waves. It was confirmed that the noise factor is dominant on all the wave conversion, growing and damping of envelopes and shocks. The presented technique in this study can be easily utilized for other nonlinear equations in applied science. Mathematics Subject Classification (2010) : 35C08, 65C20, 60H15, 35Q40, 35Q55, 35Q62 [ABSTRACT FROM AUTHOR]

The Wiener process was used to explore the (2 + 1)-dimensional chiral nonlinear Schrödinger equation (CNLSE). This model outlines the energy characteristics of quantum physics' fractional Hall effect edge states. The sine-Gordon expansion technique (SGET) was implemented to extract stochastic solutions for the CNLSE through multiplicative noise effects. This method accurately described a variety of solitary behaviors, including bright solitons, dark periodic envelopes, solitonic forms, and dissipative and dissipative–soliton-like waves, showing how the solutions changed as the values of the studied system's physical parameters were changed. The stochastic parameter was shown to affect the damping, growth, and conversion effects on the bright (dark) envelope and shock-forced oscillatory wave energy, amplitudes, and frequencies. In addition, the intensity of noise resulted in enormous periodic envelope stochastic structures and shock-forced oscillatory behaviors. The proposed technique is applicable to various energy equations in the nonlinear applied sciences. [ABSTRACT FROM AUTHOR]

Due to high rate of electrical device usage of all types and high consumption of electricity, it is necessary to search for alternative way. There are so many models of nature describing many phenomena in energy, magnetic field, heat transfer, and so on. These models are reflected in the delicate nonlinear partial differential equations. The system of coupled Konno-Oono equations is one of those models. We extract some vital solutions for this model, which describe some vital phenomena in applied science. Namely, we applied unified technique in order to perform this mechanism in a completely unified way. Finally, some simulations are performed by utilizing Matlab 18 to exhibit the behaviour of these solutions. [ABSTRACT FROM AUTHOR]

We consider the isothermal Euler model with non-vacuum initial data. We extract the Riemann invariants of the isothermal Euler model, which admits vital applications. We also design the modified Rusanov (mR) scheme to solve the isothermal Euler model. This scheme consists of two steps, the first step of the scheme depends on a local parameter allowing to control diffusion. The second stage recovers conservation equation. This technique is a straightforward to implement and precise. We compare this scheme with the Rusanov scheme via three numerical examples. This numerical study verifies the efficiency of the mR scheme. Finally, the mR scheme can be used to solve many other models in applied science. [ABSTRACT FROM AUTHOR]

Langmuir waves propagate in fractal complex plasma with fractal characteristics, which may cause some plasma particles to be trapped or causes wave turbulences. This phenomenon appears in the form of fractional order equations. Using an effective unified solver, some new solitary profiles such as rational, trigonometrically and hyperbolical functions forms are discussed, using fractional derivatives in conformable sense. The fractional order modulates the solitary properties, such as amplitudes and widths. The proposition technique can be executed to study many applied science models. [ABSTRACT FROM AUTHOR]

In this paper, we consider the fractional ion sound and Langmuir waves (FISALWs) equation. We apply the unified solver technique in order to extract some new solutions for the FISALWs equation. The fractional derivative is defined in the sense of a conformable fractional derivative. The proposed solver is based on He's semi-inverse method and gives beneficial solutions in explicit form. The recital of the method is trustworthy and useful and gives new, more general exact solutions. The constraint conditions for the existence of valid soliton solutions are reported. The enforcement of the presented solutions might be especially interesting in the applications of plasma physics such as bursty waves in cusp regions, Langmuir turbulence, and solar wind. Finally, the proposed solver can be extended to many other models in new physics and applied science. [ABSTRACT FROM AUTHOR]

In this article, we applied the unified solver method to extract stochastic solutions of a new stochastic extension of nonlinear Schrödinger equation. This solver gives the closed formula in explicit form. The acquired stochastic solutions may be applicable for explaining some phenomena in many fields of applied sciences. The presented results illustrate that the proposed solver is efficient and adequate. Moreover, the constraint conditions are utilised to verify the existence of solutions. Chi-square statistical distribution is chosen to represent the dispersion random input. In order to illustrate the dynamical behaviour of random solutions, the expectation value and their variance are depicted graphically using suitable parameters. [ABSTRACT FROM AUTHOR]

In this article, we take into account the (2 + 1) -dimensional stochastic Chiral nonlinear Schrödinger equation (2D-SCNLSE) in the Itô sense by multiplicative noise. We acquired trigonometric, rational and hyperbolic stochastic exact solutions, using three vital methods, namely Riccati–Bernoulli sub-ODE, He's variational and sine–cosine methods. These solutions may be applicable in various applications in applied science. The proposed methods are direct, efficient and powerful. Moreover, we investigate the effect of multiplicative noise on the solution for 2D-SCNLSE by introducing some graphs to illustrate the behavior of the obtained solutions. [ABSTRACT FROM AUTHOR]

We study on constructing new traveling wave solution of a system known as ion sound and Langmuir waves by using method of extended Jacobian elliptic function expansion and He's semi-inverse technique. Some new solutions will be beneficial for researchers concerning with nonlinear physical phenomena. The proposed methods may serve as the framework for solutions of various equations in applied science. Graphical simulations are provided to illustrate the behavior of these solutions. [ABSTRACT FROM AUTHOR]