New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

Düşünceli, Faruk

doi:10.2478/amns.2019.2.00031

Cited by 38 publications

(20 citation statements)

References 21 publications

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“…Several other methods including simple trigonometric ansatz methods [21,22], modified auxiliary equation technique [23,24], unified method [25,27], Jacobi elliptic function expansion method [28,29], Sine-Gordon expansion method [30,31], Exp (−ϕ(ξ ))-Expansion method [32,33], and modified simple equation method [34,35] are some other important and efficient methods to set exact solutions to nonlinear PDEs. For more details regarding models of nonlinear PDE and their solutions, one may refer to [36][37][38][39] and references therein. These methods In this article, we are concerned with implementing a new extended direct algebraic approach to derive a large family of exact solutions to both the KdV equation represented in Eq.…”

Section: Introductionmentioning

confidence: 99%

New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations

Rezazadeh

Korkmaz

Achab

et al. 2020

Applied Mathematics and Nonlinear Sciences

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A large family of explicit exact solutions to both Korteweg- de Vries and modified Korteweg- de Vries equations are determined by the implementation of the new extended direct algebraic method. The procedure starts by reducing both equations to related ODEs by compatible travelling wave transforms. The balance between the highest degree nonlinear and highest order derivative terms gives the degree of the finite series. Substitution of the assumed solution and some algebra results in a system of equations are found. The relation between the parameters is determined by solving this system. The solutions of travelling wave forms determined by the application of the approach are represented in explicit functions of some generalized trigonometric and hyperbolic functions and exponential function. Some more solutions with different characteristics are also found.

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Section: Introductionmentioning

confidence: 99%

New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations

Rezazadeh

Korkmaz

Achab

et al. 2020

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

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“…There are several approaches for finding solutions of nonlinear partial differential equations which have been developed and employed successfully. Some of these are a new sub equation method [1], homotopy analysis method [2,3], homotopy-Pade method [4], homotopy perturbation method [5,6], (G ′ /G)-expansion method [7,8], modified variational iteration algorithm-I [9,10,11], sub equation method [12], Variational iteration method with an auxiliary parameter [13,14,15,16], sumudu transform approach [17], (1/G ′ )-expansion method [18,19], variational iteration method [20,21], auto-Bäcklund transformation method [22], Clarkson-Kruskal direct method [23], Bernoulli sub-equation function technique [24], decomposition method [25,26,27,28], modified variational iteration algorithm-II [29,30,31], first integral method [32], homogeneous balance method [33], modified Kudryashov technique [34], residual power series approach [35], collocation method [36], extended rational SGEEM [37], sine-Gordon expansion method [38,39] and many more [40,41,...…”

Section: Introductionmentioning

confidence: 99%

Hyperbolic Type Solutions for the Couple Boiti-Leon-Pempinelli System

2020

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In this paper, the (1/G')-expansion method is used to solve the coupled Boiti-Leon-Pempinelli (CBLP) system. The proposed method was used to construct hyperbolic type solutions of the nonlinear evolution equations. To asses the applicability and effectiveness of this method, some nonlinear evolution equations have been investigated in this study. It is shown that with the help of symbolic computation, the (1/G')-expansion method provides a powerful and straightforward mathematical tool for solving nonlinear partial differential equations.

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“…31 In subsequent studies, other researchers at the Flemish Electromechanical Technology Centre conducted research on the optimization of badminton robot movement trajectory time and made some progress. [32][33][34][35] The research of badminton robots in society can solve obstacles such as difficult golfers, difficult time coordination, and limited venues for badminton enthusiasts, and improve people's sports experience. 36 This will improve the participation of the whole people, increase the time of national sports, and enhance the physical fitness of the people and actively promote its role.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Simulation of Badminton Robot Based on Fractal Brown Motion

2020

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This paper focuses on the design of badminton robots, and designs high-precision binocular stereo vision synchronous acquisition system hardware and multithreaded acquisition programs to ensure the left and right camera exposure synchronization and timely reading of data. Aiming at specific weak moving targets, a shape-based Brown motion model based on dynamic threshold adjustment based on singular value decomposition is proposed, and a discriminative threshold is set according to the similarity between the background and the foreground to improve detection accuracy. The three-dimensional trajectory points are extended by Kalman filter and the kinematics equation of badminton is established. The parameters of the kinematics equation of badminton are solved by the method of least squares. Based on the fractal Brownian motion algorithm, a real-time robot pose estimation algorithm is proposed to realize the real-time accurate pose estimation of the robot. A PID control model for the badminton robot executive mechanism is established between the omnidirectional wheel speed and the robot’s translation and rotation movements to achieve the precise movement of the badminton robot. All the algorithms can meet the system’s requirements for real-time performance, realize the badminton robot’s simple hit to the ball, and prospect the future research direction.

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New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

Cited by 38 publications

References 21 publications

New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations

New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations

Hyperbolic Type Solutions for the Couple Boiti-Leon-Pempinelli System

Trajectory Simulation of Badminton Robot Based on Fractal Brown Motion

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