Unstable Media Research Articles

Optical soliton solutions and modulation instability for unstable conformable Schrödinger model

The unstable time fractional Schrödinger model (UTFSM) is studied through the development of disturbances in marginally stable or unstable media. A modified Sardar-sub equation technique (MSSE) for a conformable fractional-order nonlinear evolution model is presented in this paper. The objective here is to construct new wave solutions for UTFSM. These solutions have particular relevance in quantum physics and assume several forms such as rational, exponential, trigonometric and hyperbolic functions, as well as combo solutions. This technique produces various shapes of dark, kink-type solitons and periodic solitary waves by setting proper parametric values. These discrete physical frameworks contribute to an understanding from analysis of unstable dynamical models. Additionally, we investigate modulation instability and stability analysis to ensure that obtained solutions are highly stable. The multiplicity of waves and solutions emphasizes how this technique can be used for different nonlinear fractional models in quantum physics and other areas.

Large field of view multi-point light focusing in strongly perturbed scattering media based on non-dominated bat algorithm wavefront shaping

Wavefront shaping has become a powerful tool for controlling light through scattering media and enable the focusing and imaging of diffusive light. However, when facing with strong noise environments or scattering media being suddenly disturbed, this method becomes powerless. In addition, due to limitations of memory effects (ME) range, the field of view for imaging is very small. In this paper, we propose a new non-dominated bat algorithm (N-BA) for wavefront shaping multi-point optical focusing with adaptive mutation rate, which can easily change the mutation rate in the iterative process by calculating the error rate of the current solution to adapt to sudden strong scattering media disturbances. Experimental results show that when the scattering medium is disturbed and the focusing performance significantly deteriorates, the proposed method can effectively achieve multi-point focusing with large field of view and uniform intensity. We believe that this research may promote or stimulate more applications of wavefront shaping in unstable media and even living biological tissues.

Solitary and periodic wave solutions of the unstable nonlinear Schrödinger’s equation

Solving partial differential equations has always been one of the significant mathematical tools for modeling applied phenomena in various fields. In this paper, our main motivation is to find the traveling wave solutions of unstable nonlinear Schrödinger equation (UNLSE) which describes the two layer baroclinic instability, and two lossless symmetric stream plasma instability, and also disturbance of time period in both stable and unstable media. The methods which are used to endure these solutions are extended rational sine-cosine/sinh-cosh. New solutions are constructed in the different forms such as hyperbolic and trigonometric. The achieved results present that proposed techniques are consequential for exploring several types of nonlinear partial differential equations (NLPDEs) in applied sciences and solutions are presented in the form of novel periodic, dark, bright, and periodically bright solitons. These methods are highly effective, robust, and provide an alternative approach for establishing new soliton solutions for various types of partial differential equations (PDEs) used in mathematical physics.

Abundant solitary wave solutions for space-time fractional unstable nonlinear Schrödinger equations and their applications

The unstable nonlinear Schrödinger models illustrate the time evolution of disturbances in marginally stable or unstable media. In this article, an improved auxiliary equation method is proposed for conformable fractional-order nonlinear evolution equations to obtain the novel wave solutions of space–time fractional unstable and modified unstable nonlinear Schrödinger equations. Several types of novel wave solutions are constructed in forms of some special Jacobi elliptic functions, rational, exponential, trigonometric and hyperbolic functions in which various are unique and having key utilization in quantum physics. With the aid of appropriate values to parameters, different shapes of bright, dark, kink type soliton, multi-peak solitons, periodic solitary waves etc. are depicted. These distinct physical structures are helpful in the understanding the complex physical interpretation of unstable dynamical models. Furthermore, this article gives an idea, how can reduce the conformable fractional order unstable nonlinear Schrödinger equations into an ODE of one variable to obtain the exact solutions. The numerous obtained waves and other solutions reveal the usefulness of the proposed technique which can be utilized to other nonlinear fractional models arising in quantum physics and other fields of applied sciences.

Construction of Novel Bright-Dark Solitons and Breather Waves of Unstable Nonlinear Schrödinger Equations with Applications

The unstable nonlinear Schrödinger equations (UNLSEs) are universal equations of the class of nonlinear integrable systems, which reveal the temporal changing of disruption in slightly stable and unstable media. In current paper, an improved auxiliary equation technique is proposed to obtain the wave results of UNLSE and modified UNLSE. Numerous varieties of results are generated in the mode of some special Jacobi elliptic functions and trigonometric and hyperbolic functions, many of which are distinctive and have significant applications such as pulse propagation in optical fibers. The exact soliton solutions also give information on the soliton interaction in unstable media. Furthermore, with the assistance of the suitable parameter values, various kinds of structures such as bright-dark, multi-wave structures, breather and kink-type solitons, and several periodic solitary waves are depicted that aid in the understanding of the physical interpretation of unstable nonlinear models. The various constructed solutions demonstrate the effectiveness of the suggested approach, which proves that the current technique may be applied to other nonlinear physical problems encountered in mathematical physics.

Computational techniques to study the dynamics of generalized unstable nonlinear Schrödinger equation

In this paper, a more general form of unstable nonlinear Schrödinger equation which describe the time evolution of disturbances in marginally stable or unstable media is studied. A new modification of the Sardar sub-equation method is discussed and employed to retrieve solitons and other solutions of the suggested nonlinear model. A variety of solutions, including bright solitons, dark solitons, singular solitons, combo bright-singular solitons, periodic, exponential, and rational solutions are provided with considerable physical perspective. Using the q-homotopy analysis algorithm in combination with the Laplace transform, we present the approximate solutions of the bright and dark solitons, including the physical nature of the attained solutions. The computation complexity and results indicate that the given techniques are simple, effective, uncomplicated, and that they may be used to a wide range of unstable and stable nonlinear evolution equations encountered in mathematics, mathematical physics, and other applied disciplines.

Extracting novel categories of analytical wave solutions to a nonlinear Schrödinger equation of unstable type

Solving partial differential equations has always been one of the significant tools in mathematics for modeling applied phenomena. In this paper, using an efficient analytical technique, exact solutions for the unstable Schrödinger equation are constructed. This type of the Schrödinger equation describes the disturbance of time period in slightly stable and unstable media and manages the instabilities of lossless symmetric two stream plasma and two layer baroclinic. The basis of this method is the generalization of some commonly used methods in the literature. To better demonstrate the results, we perform many numerical simulations corresponding to the solutions. All these solutions are new achievements for this form of the equation that have not been acquired in previous research. As one of the strengths of the article, it can be pointed out that not only is the method very straightforward, but also can be used without the common computational complexities observed in known analytical methods. In addition, during the use of the method, an analytical solution is obtained in terms of familiar elementary functions, which will make their use in practical applications very convenient. On the other hand, the utilized methodology empowers us to handle other types of well-known models. All numerical results and simulations in this article have been obtained using computational packages in Wolfram Mathematica.

Construction of soliton solutions of the modify unstable nonlinear Schrödinger dynamical equation in fiber optics

In this research article, we investigated the universal model of integrable system of modify unstable nonlinear Schrodinger equation. The mUNLSE described the disturbance of time period in slightly stable and unstable media and managed the instability of modulation wave train. We found the exact and solitary wave solutions of mUNLSE with the help of modified extended auxiliary equation mapping method. As a result, exact and solitary wave solutions in the form of elliptic functions, trigonometric functions, hyperbolic functions, bright and dark solitons, traveling wave, kink-type solitons and periodic solitary wave solution are obtained. These solutions show the power and effectiveness of this new method and two- and three-dimensional graphically with the help of computer software Mathematica. We can also solve other unstable nonlinear system of PDEs which are involved in Mathematical physics and many other branches of physical sciences with the help of this new method.

The modify unstable nonlinear Schrödinger dynamical equation and its optical soliton solutions

In this research, we work on a specific class of nonlinear evolution equation which is the modify unstable nonlinear Schrodinger equation. This equation is used to describe a time evolution of disturbances in unstable media. Various solutions have been obtained. The results deduced are of varied types and include bright solution, dark solution, rational dark-bright solution, as well as cnoidal solutions. These solutions might be useful in engineering fields. Some conditions for the stability of these solutions are presented. The method used here is understandable and very powerful for solving the nonlinear problems.

New explicit exact solutions of the unstable nonlinear Schrödinger’s equation using the exp a and hyperbolic function methods

Under investigation in the present work is to study the unstable nonlinear Schrodinger’s equation which points out the time evolution of disturbances in marginally stable or unstable media. The exp a and hyperbolic function methods are adopted to carry out this target in a straightforward way. A wide variety of new explicit exact solutions are successfully derived, proving the excellent performance of the schemes.

Bright–dark solitary wave and elliptic function solutions of unstable nonlinear Schrödinger equation and their applications

In this article, we study the unstable nonlinear Schrodinger equation (UNLSE). Analytically by modified extended direct algebraic method, which describes the disturbances in time evolution of marginally stable or unstable media. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave and elliptic function solutions of UNLSE. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomenas of this unstable equation. Moreover, we also present the formation conditions of the bright and dark solitons of UNLSE. The obtained results and computational work shows the power and effectiveness of this method. Many other such types of nonlinear evolution equations arising in engineering, applied sciences and nonlinear optics can also be solved by this method.

New Exact Traveling Wave Solutions of the Unstable Nonlinear Schrödinger Equations

The present paper studies the unstable nonlinear Schrödinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schrödinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schrödinger equation and its modified form are formally obtained.

Optical soliton solutions of unstable nonlinear Schröodinger dynamical equation and stability analysis with applications

In optical solitons, the propagation is usually governed by the nonlinear Schrödinger equations. In nonlinear Schrödinger equations (NLSEs), the unstable NLSE is a universal equation of the class of nonlinear integrable systems, which describes the disturbances in time evolution of marginally stable or unstable media. The aim of this article is to study the unstable NLSE analytically. Several explicit new exact solutions such as soliton, solitary wave, elliptic function and periodic solutions of unstable NLSE are constructed by using proposed modified extended mapping method, which have important applications in applied science and engineering. The movement of obtained soliton solutions are presented graphically, which helps to understand the physical phenomenas of the unstable equation. The stability analysis of the constructed solutions and the movement role of waves are examined by employing modulation instability analysis. All solutions are stable and analytical.

Applications of extended simple equation method on unstable nonlinear Schrödinger equations

The unstable nonlinear Schrödinger equations describe the time evolution of disturbances in marginally stable or unstable media. In this paper, the extended form of simple equation method (SEM) is employed to construct exact travelling wave solutions of unstable nonlinear schröodinger equation and modify unstable nonlinear schrödinger equation. The exact solutions are obtained in the form of trigonometric, hyperbolic, exponential and rational functions in which some of them are new. The movements of these solutions are shown graphically. The computational work and obtained results show that the presented method is simple, effective and straightforward, and can be employed to many other types of unstable nonlinear evolution equations arising in mathematics, mathematical physics and other areas of applied sciences.

Modulation instability analysis of modify unstable nonlinear schrodinger dynamical equation and its optical soliton solutions

Abstract The nonlinear Schrodinger equations (NLSEs) describe the promulgation of ultra-short pluse in optical fibers. The modify unstable nonlinear Schrodinger equation (mUNLSE) is a universal equation of the class of nonlinear integrable systems in NLSEs, which governs certain instabilities of modulated wave-trains. This equation also describes the time evolution of disturbances in marginally stable or unstable media. In the current work, the aim is to investigate the mUNLSE analytically by utilizing proposed modified extended mapping method. New exact solutions are constructed in the different form such as exact dark soliton, exact bright soliton, bright-dark soliton, solitary wave, elliptic function in different form and periodic solutions of mUNLSE. Furthermore, we also present the formation conditions of the bright soliton and dark soliton of this equation. The modulation instability analysis is implemented to discuss the stability analysis of the attained solutions and the movement role of the waves is examined, which confirms that all constructed solutions are exact and stable.

The stability and degradation kinetics of acetylsalicylic acid in different organic solutions revisited – an UHPLC–ESI-QTOF spectrometry study

Abstract Ultra high performance liquid chromatography (UHPLC), coupled with accurate quadrupole-time-of-flight (Q-TOF) mass spectrometry, was used for the stability study of acetylsalicylic acid within a variety of different organic solutions: methanol, ethanol, propan-2-ol, acetonitrile, tetrahydrofuran and 1,4-dioxane. With the use of gradient elution chromatography and mass spectrometry detection in negative ionization, MS and MS/MS spectra were recorded simultaneously. In addition, quantitative, as well as qualitative analysis was performed during one assay. The stability of acetylsalicylic acid in such solutions was tested at room temperature, in a 12h period. In the work, in all cases, only one main degradation product, salicylic acid, was found. What is more, the work revealed that the degradation of aspirin in the tested organic solutions yields apparent second-order kinetics. The study also demonstrated that acetonitrile and 1,4-dioxane turned out to be the most stable solvents, and an above 80% of initial concentration of acetylsalicylic acid was found in this case. Furthermore, the most popular analytical solvents, methanol and ethanol, were found to be very unstable media. Herein, below 40% of initial concentration of acetylsalicylic acid was seen after 12h. The obtained results were also compared with the degradation of acetylsalicylic acid in a water solution. In this situation, only about 25% of the analyzed compound was resolved to salicylic acid in the same time frame.

A deformation/blurring-based spatio-temporal model

A key objective in spatio-temporal modeling consists of providing an appropriate representation of complexity in interactive spatio-temporal dynamics inherent to real phenomena. Propagated effect of dynamical spatial deformation provides a meaningful way to describe certain forms of heterogeneous behaviour; in particular, in relation to processes evolving in unstable media, or to account for the possible effect of covariates, to mention some significant interpretations. In this paper, the formulation of a discrete time and continuous space spatio-temporal interaction model with autoregressive dynamics, incorporating the effect of continuous deformation of the spatial support over time, is studied. Among other fields, this approach provides a suitable representation for a variety of geophysical and environmental applications. In particular, a vast family of heterogeneous models is generated from models which display homogeneity in the absence of deformation. Structural characteristics and variability properties, as well as self-consistency conditions for a limiting continuous-time approximation, are analyzed.

Relativistic generalization of quasi-Chaplygin equations

A relativistic generalization of quasi-Chaplygin (quasi-gas) equations describing the evolution of unstable media with negative compressibility is proposed. Examples of the media whose dynamics can be described by the proposed equations are considered. An analytic solution to these nonlinear equations is obtained for the 1D case.

Three-wave resonant interactions in unstable media

We consider the evolution of weakly nonlinear disturbances in linearly unstable stratified shear flows. We develop a generic Hamiltonian formulation for two-dimensional flows. The paper is focused on three-wave resonant interactions, which are always present in the stratified shear flows under consideration as the lowest-order nonlinear process. Two different types of shear flows are considered. The first one is the classical piecewise-linear model with constant density and vorticity in each layer. For such flows, linear instability is due to weak interaction of different modes. The second type is the Kelvin-Helmholtz model, consisting of two layers with different densities and velocities. Velocity shear is assumed to be weakly supercritical. We show that apart from the classical triplets consisting of stable waves, both flow types admit only triplets consisting of one weakly unstable and two neutrally stable waves, and we consider them in detail. Universal evolution equations for three resonantly interacting wave packets are derived for both cases

Symmetries and invariant solutions of absolutely unstable media equations

An algorithm for constructing fundamental solutions by using symmetries is proposed. The symmetries and the periodic invariant solutions of absolutely unstable media equations are found.