New Optical Soliton Solutions for Coupled Resonant Davey-Stewartson System with Conformable Operator

2021 ◽  
Author(s):  
Shrideh Al-Omari ◽  
Mohammed Alabedalhadi ◽  
Mohammed Al-Smadi ◽  
Shaher Momani
Keyword(s):  
Soliton Solutions ◽  
Rational Functions ◽  
Dark Soliton ◽  
Wave Transformation ◽  
Order System ◽  
The Novel ◽  
Integer Order ◽  
Governing System ◽  
Conformable Derivatives ◽  
Fractional Orders

Abstract This paper investigates the novel soliton solutions of the coupled fractional system of the resonant Davey-Stewartson equations. The fractional derivatives are considered in terms of conformable sense. Accordingly, we utilize a complex traveling wave transformation to reduce the proposed system to an integer-order system of ordinary differential equations. The phase portrait and the equilibria of the obtained integer-order ordinary differential system will be studied. Using suitable mathematical assumptions, the new types of bright, singular, and dark soliton solutions are derived and established in view of the hyperbolic, trigonometric, and rational functions of the governing system. To achieve this, illustrative examples of the fractional Davey-Stewartson system are provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of conformable derivatives on behavior of acquired solutions for different fractional orders is also discussed. By comparing the proposed method with the other existing methods, the results show that the execute of this method is concise, simple, and straightforward. The results are useful for obtaining and explaining some new soliton phenomena.

Synchronization and Antisynchronization of a Class of Chaotic Systems With Nonidentical Orders and Uncertain Parameters

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Diyi Chen ◽  
Weili Zhao ◽  
Xinzhi Liu ◽  
Xiaoyi Ma
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Order System ◽  
Theory Analysis ◽  
Integer Order ◽  
Uncertain Chaotic Systems ◽  
Hyperchaotic Systems ◽  
Fractional Orders ◽  
Good Agreement

In this paper, we study the synchronization of a class of uncertain chaotic systems. Based on the sliding mode control and stability theory in fractional calculus, a new controller is designed to achieve synchronization. Examples are presented to illustrate the effectiveness of the proposed controller, like the synchronization between an integer-order system and a fraction-order system, the synchronization between two fractional-order hyperchaotic systems (FOHS) with nonidentical fractional orders, the antisynchronization between an integer-order system and a fraction-order system, the synchronization between two new nonautonomous systems. The simulation results are in good agreement with the theory analysis and it is noted that the proposed control method is of vital importance for practical system parameters are uncertain and imprecise.

scholarly journals Coexisting Three-Scroll and Four-Scroll Chaotic Attractors in a Fractional-Order System by a Three-Scroll Integer-Order Memristive Chaotic System and Chaos Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Xikui Hu ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Control ◽  
Initial Conditions ◽  
Fractional Order System ◽  
Order System ◽  
Chaotic Attractors ◽  
Integer Order ◽  
Memristive System ◽  
Fractional Orders

Based on the integer-order memristive system that can generate two-scroll, three-scroll, and four-scroll chaotic attractors, in this paper, we found other phenomena that two kinds of three-scroll chaotic attractors coexist in this system with different initial conditions. Furthermore, we proposed a coexisting fractional-order system based on the three-scroll chaotic attractors system, in which the three-scroll or four-scroll chaotic attractors emerged with different fractional-orders q. Meanwhile, with fractional-order q=0.965 and different initial conditions, coexistence of two kinds of three-scroll and four-scroll chaotic attractors is found simultaneously. Finally, we discussed controlling chaos for the fractional-order memristive chaotic system.

scholarly journals Discrete Bright-dark Soliton Interaction Dynamic Behaviors for Nonautonomous 2+1-Dimensional Soliton Equation

2021 ◽  
Author(s):  
Li Li ◽  
fajun yu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
The Novel ◽  
Optical Fields ◽  
Dynamic Behaviors ◽  
Spatial Part ◽  
Bright Soliton Solution ◽  
Temporal Parts ◽  
Interaction Dynamic

Abstract The non-autonomous discrete bright-dark soliton solutions(NDBDSSs) of the 2+1-dimensional Ablowitz-Ladik(AL) equation are derived. We analyze the dynamic behaviors and interactions of the obtained 2+1-dimensional NDBDSSs. In this paper, we present two kinds of different methods to control the 2+1-dimensional NDBDSSs. In first method, we can only control the wave propagations through the spatial part, since the time function has not effect in the phase part. In second method, we can control the wave propagations through both the spatial and temporal parts. The different propagation phenomena can also be produced through two kinds of managements. We obtain the novel "л"-shape non-autonomous discrete bright soliton solution(NDBSS), the novel "λ"-shape non-autonomous discrete dark soliton solution(NDDSS) and their interaction behaviors. The novel behaviors are considered analytically, which can be applied to the electrical and optical fields.

scholarly journals Two Reliable Methods for Solving the (3 + 1)-Dimensional Space-Time Fractional Jimbo-Miwa Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-30 ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert ◽  
Chaowanee Khaopant ◽  
Wanassanun Porka
Keyword(s):  
Exact Solutions ◽  
Dimensional Space ◽  
Soliton Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Space Time ◽  
The Novel ◽  
Wave Solutions ◽  
Liouville Derivative

We investigate methods for obtaining exact solutions of the (3 + 1)-dimensional nonlinear space-time fractional Jimbo-Miwa equation in the sense of the modified Riemann-Liouville derivative. The methods employed to analytically solve the equation are the G′/G,1/G-expansion method and the novel G′/G-expansion method. To the best of our knowledge, there are no researchers who have applied these methods to obtain exact solutions of the equation. The application of the methods is simple, elegant, efficient, and trustworthy. In particular, applying the novel G′/G-expansion method to the equation, we obtain more exact solutions than using other existing methods such as the G′/G-expansion method and the exp-Φ(ξ)-expansion method. The exact solutions of the equation, obtained using the two methods, can be categorized in terms of hyperbolic, trigonometric, and rational functions. Some of the results obtained by the two methods are new and reported here for the first time. In addition, the obtained exact explicit solutions of the equation characterize many physical meanings such as soliton solitary wave solutions, periodic wave solutions, and singular multiple-soliton solutions.

Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines

2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Auxiliary Equation ◽  
Discussion Section ◽  
Auxiliary Equation Method ◽  
Advantages And Disadvantages

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.

An explicit plethora of soliton solutions for a new microtubules transmission lines model: A fractional comparison

2021 ◽  
Author(s):  
Nauman Raza ◽  
Ziyad A. Alhussain
Keyword(s):  
Nonlinear Dynamics ◽  
Transmission Lines ◽  
Fractional Derivatives ◽  
Intracellular Transport ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Governing System ◽  
Parameter Values ◽  
Fractional Parameter

This paper introduces a new fractional electrical microtubules transmission lines model in the sense of Atangana–Baleanu and beta derivatives to comprehend nonlinear dynamics of the governing system. This structure possesses one of the most important parts in cellular process biology and fractional parameter incorporates the memory effects in microtubules. Also, microtubules are extremely beneficial in cell motility, signaling and intracellular transport. The new extended direct algebraic method is a compelling and persuasive integrating scheme to extract soliton solutions. The retrieved solutions include dark, bright and singular solitons. This model executes a prominent part in exhibiting the wave transmission in nonlinear systems. The novelty and advantage of the proposed method are portrayed by applying it to this model and its dynamical behavior is depicted by 3D and 2D plots. A comparative study of two fractional derivatives at distinct fractional parameter values and graphics of sensitivity analysis is also carried out in this paper.

Oblique nonlinear Alfvén waves in strongly magnetized beam plasmas. Part 2. Soliton solutions and integrability

1993 ◽  
Vol 50 (3) ◽  
pp. 457-476 ◽  
Author(s):  
Bernard Deconinck ◽  
Peter Meuris ◽  
Frank Verheest
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Mhd Waves ◽  
Displacement Current ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.

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