On complex wave solutions governed by the 2D Ginzburg–Landau equation with variable coefficients

Complex wave solutions described by a (3+1)-dimensional coupled nonlinear Schrödinger equation with variable coefficients

Some new exact solutions of the generalized (3 + 1)-dimensional Kadomtsev-Petviashvili equation (KPE) are explored in this study. Firstly, the resonant multiple soltion solutions (RMSs) are discussed via employing the linear superposition principle and weight algorithm. Then, by introducing pairs of the conjugate parameters to the RMSs, the complexiton solutions including the non-singular complexiton and singular complexiton solutions are extracted. In addition, the complex multiple kink soliton solutions are also probed by employing the bilinear approach. Finally, we investigate the rational wave solutions via the test function method and symbolic computation. By choosing the appropriate parameters, the graph descriptions of the derived solutions are presented to show the dynamical properties. The outcomes of this work are desirous to bring some new perspective to the study of the complexiton, complex solutions and rational wave solutions to the other PDEs.

This paper extracts entirely new complex logarithmic prototypes to the nonlinear Black–Scholes equation used to investigate the price in economy. Newly submitted to the literature, [Formula: see text]-expansion method is used, successfully. Complex, logarithmic and hyperbolic non-traveling wave solutions are extracted to the considered model. Examined is the solution’s response for various conformable operator values. To verify the sensitivity of the numerical outcomes, tables with the stability and absolute error analysis findings are also provided. Von Neumann Stability analysis looks at the circumstances in which the model’s numerical findings are stable. Critical features, such as stability analysis and error evaluation, are presented, providing comprehensive information on the reliability and accuracy of the method. Errors that arise during the approximation process and the impact of parameter values are displayed through tables and graphs when employing the numerical technique. It offers a thorough comprehension of the financial phenomenon that the model under examination represents.

On complex soliton solutions, complex elliptic solutions and complex rational function solutions for the Sasa-Satsuma model equation with variable coefficients

In this study, the new complex wave solutions of the perturbed Fokas-Lenells (p-FL) equation, which has applications in nonlinear optical fibers are obtained using a new extended direct algebraic method. This model represents recent electronic communications like Internet blogs, facebook communication and twitter comments. The obtained solutions are the different classes of traveling wave structures with singular solutions Type-I & II, dark-singular, dark, and dark-bright solutions. Furthermore, stability conditions for the computed structures are reported. Also, graphical representations of some particular structures are shown by taking the specific values of the constants. The ordinary differential equation (ODE) obtained from a traveling wave transformation is converted into a dynamical system using Galilean transformation. The phase plane analysis is done for different values of the controlled parameters d 1 and d 3. A perturbation term is added to analyze the chaotic dynamics, and plots indicate that the system shows the chaotic dynamics. Also, sensitivity analysis shows that the system is sensitive to initial conditions. The conclusion is accounted for toward the end.

On complex wave solutions for the variable-coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

In this article, the unified method, the improved F-expansion method and the modified Kudryashov method are used to obtain the traveling wave solutions of the generalized Zakharov–Kuznetsov equation with variable coefficients. Different types of traveling wave solutions are derived including polynomial solutions and rational solutions by applying the unified method. The polynomial solutions include solitary wave solutions, soliton wave solutions and elliptic wave solutions, and the rational solutions contain periodic type rational solutions and soliton type rational solutions. By means of the improved F-expansion method with Riccati equation, the hyperbolic trigonometric solutions, trigonometric solutions and rational solutions are obtained containing several free parameters. The modified Kudryashov method is also applied to obtain new traveling wave solutions. In addition, the properties of several solutions are represented graphically with the appropriate parameters.

With the evolution in the information transmission technologies and rapidly augmenting requirement for high-speed, readily available, and long-haul links, optical communication is witnessed as one of the most prominent solutions to tackle to ever-growing user's demands. Optical communication links are further classified as optical fiber and optical wireless links based on the medium of information propagation. Optical wireless communication (OWC) links, which use free space as the propagation medium have gathered significant attraction nowadays because of it easy deployment and low cost installation process. One of the most crucial applications of OWC links is the transmission of information between two or more satellites, also referred to as inter-satellite optical wireless communication (IsOWC) link. In this work, we propose modeling and analysis of a 10 Gbps long-haul IsOWC link by incorporating Manchester encoding for improved link performance. Furthermore, the impact of increasing link distance, pointing errors, laser transmission power, and receiver lens diameter is investigated and faithful 18000 km-10 Gbps information transmission is reported.

The National Aeronautics and Space Administration (NASA) Glenn Research Center (GRC) has developed a laboratory transmitter and receiver prototype of a space-to-ground optical communications link. The system is meant to emulate future deep space optical communication links, such as the first crewed flight of Orion, in which the transmitted laser is modulated using pulse position modulation and the receiver is capable of detecting single photons. The transmitter prototype consists of a software defined radio, a high extinction ratio electro-optic modulator system, and a 1550 nm laser. The receiver is a scalable concept and utilizes a single-pixel array of fiber coupled superconducting nanowire single photon detectors. The transmit and receive waveforms follow the Consultative Committee for Space Data Systems (CCSDS) Optical Communications Coding and Synchronization Standard. A software model of the optical transmitter and receiver has also been implemented to predict performance of the optical test bed. This paper describes the transmitter and receiver prototypes as well as the system test configuration. System level tests results are presented and shown to align with predictions from software simulations. The validated software model can be used to in the future to reduce the design cycle of optical communications systems.

The Ablowitz–Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyperbolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz–Ladik equation are derived by using the (G′/G)-expansion method, and the effects of the parameters (including the coupling constant and other parameters) on the linear stability of the exact solutions are analysed and numerically simulated.

PurposeThe purpose of this paper is to introduce a variety of new completely integrable Calogero–Bogoyavlenskii–Schiff (CBS) equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for each of the developed models.Design/methodology/approachThe newly developed models with time-dependent coefficients have been handled by using the simplified Hirota’s method. Moreover, multiple complex soliton solutions are derived by using complex Hirota’s criteria.FindingsThe developed models exhibit complete integrability, for specific determined functions, by investigating the compatibility conditions for each model.Research limitations/implicationsThe paper presents an efficient algorithm for handling integrable equations with analytic time-dependent coefficients.Practical implicationsThe work presents new integrable equations with a variety of time-dependent coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions.Social implicationsThis study presents useful algorithms for finding and studying integrable equations with time-dependent coefficients.Originality/valueThe paper gives new integrable CBS equations which appear in propagation of waves and provide a variety of multiple real and complex soliton solutions.

Purpose The purpose of this paper is concerned with investigating three integrable shallow water waves equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for these three models. Design/methodology/approach The newly developed equations with time-dependent coefficients have been handled by using Hirota’s direct method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions. Findings The developed integrable models exhibit complete integrability for any analytic time-dependent coefficients defined though compatibility conditions. Research limitations/implications The paper presents an efficient algorithm for handling time-dependent integrable equations with analytic time-dependent coefficients. Practical implications This study introduces three new integrable shallow water waves equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author shows that integrable equations with time-dependent coefficients give real and complex soliton solutions. Social implications The paper presents useful algorithms for finding integrable equations with time-dependent coefficients. Originality/value The paper presents an original work with a variety of useful findings.

Satellite communication is one of the pioneer technologies to provide seamless communication across the globe. With large number of satellites deployed in the space, inter-satellite communication has become an important phenomenon for researchers to establish communication link between satellites. In this work, a cost-effective inter-satellite communication system is proposed by using spectral amplitude coding based on optical code division multiplex access technique and polarization division multiplexing scheme. Ten channels, each carrying 10 Gbps non-return to zero encoded data, are transmitted over 25,000 km inter-satellite optical wireless communication (Is-OWC) link. Furthermore, Is-OWC is subjected to space turbulences such as transmitting and pointing errors. The reported results show the successful transmission of 100 Gbps data over Is-OWC link.

In the inter-satellite laser communication, a reliable communication link requires the boresight tracking accuracy between the optical transceivers to be sub-micro radians, and the control error caused by the vibration of the satellite platform is the most important factor affecting the optical communication link. The vibration and the effect of the adopted suppression scheme largely determine the tracking accuracy of the PAT system. Therefore, the impact of reducing the vibration on the optical communication link is a prerequisite for establishing stable satellite optical communication links. This paper uses the active compensation of the satellite platform vibration as the research direction, and proposes a composite control micro-vibration suppression algorithm based on the RBF neural network. On the basis of traditional PID control, adaptive RBF neural network feedforward control and PID control combination constitute composite control, design and establishing satellite platform vibration suppression system, simulation verifies the performance of traditional PID control and RBF composite control algorithm, result indicates that the RBF composite control algorithm has increased by 80% compared to traditional PID control.

The modified auxiliary equation method to investigate solutions of the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity