scholarly journals Algebraic Structure and Poisson Integral Method of Snake-Like Robot Systems

2021 ◽  
Vol 9 ◽  
Author(s):  
Fu Jing-Li ◽  
Xiang Chun ◽  
Meng Lei
Keyword(s):  
Algebraic Structure ◽  
Integral Method ◽  
Hamiltonian Function ◽  
First Integral ◽  
Poisson Integral ◽  
Integral Methods ◽  
Robot Systems ◽  
Generalized Momentum ◽  
Algebraic Forms

The algebraic structure and Poisson's integral of snake-like robot systems are studied. The generalized momentum, Hamiltonian function, generalized Hamilton canonical equations, and their contravariant algebraic forms are obtained for snake-like robot systems. The Lie-admissible algebra structures of the snake-like robot systems are proved and partial Poisson integral methods are applied to the snake-like robot systems. The first integral methods of the snake-like robot systems are given. An example is given to illustrate the results.

scholarly journals The First Integral Method for Solving Maccari’s System

2011 ◽  
Vol 02 (02) ◽  
pp. 258-263 ◽  
Author(s):  
Davood Rostamy ◽  
Fatemeh Zabihi ◽  
Kobra Karimi ◽  
Siamak Khalehoghli
Keyword(s):  
Integral Method ◽  
First Integral ◽  
First Integral Method

scholarly journals Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoxiao Zheng ◽  
Yadong Shang ◽  
Yong Huang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Constant Coefficient ◽  
Wave Solution ◽  
Integral Method ◽  
Solitary Wave Solution ◽  
First Integral ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
First Integral Method

This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.

scholarly journals The first integral method and traveling wave solutions to Davey–Stewartson equation

2012 ◽  
Vol 17 (2) ◽  
pp. 182-193 ◽  
Author(s):  
Hossein Jafari ◽  
Atefe Sooraki ◽  
Yahya Talebi ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
First Integral Method ◽  
Wave Solutions

In this paper, the first integral method will be applied to integrate the Davey–Stewartson’s equation. Using this method, a few exact solutions will be obtained using ideas from the theory of commutative algebra. Finally, soliton solution will also be obtained using the traveling wave hypothesis.

First integral method for non-linear differential equations with conformable derivative

2018 ◽  
Vol 13 (1) ◽  
pp. 14 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J.F. Gómez-Aguilar ◽  
Abdon Atangana
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Integral Method ◽  
General Scheme ◽  
First Integral ◽  
Fractional Partial Differential Equations ◽  
Conformable Derivative ◽  
First Integral Method ◽  
Analytic Treatment ◽  
Linear Differential

In this paper, we present an analysis based on the first integral method in order to construct exact solutions of the nonlinear fractional partial differential equations (FPDE) described by beta-derivative. A general scheme to find the approximated solutions of the nonlinear FPDE is showed. The results obtained showed that the first integral method is an efficient technique for analytic treatment of nonlinear beta-derivative FPDE.

Optical solitons for coupled Fokas–Lenells equation in birefringence fibers

2019 ◽  
Vol 33 (26) ◽  
pp. 1950317 ◽  
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Sultan Sial
Keyword(s):  
Integral Method ◽  
Expansion Method ◽  
First Integral ◽  
Optical Solitons ◽  
Optical Soliton ◽  
First Integral Method ◽  
Complexiton Solutions ◽  
Existence Criterion

This paper discusses bright, dark and singular optical soliton as well as complexiton solutions to the coupled Fokas–Lenells equation (FLE) for birefringent fibers by three integration tools such as [Formula: see text]-expansion method, the first integral method and the sine-Gordon expansion method. The existence criterion of these solutions is also given.

Nonisothermal reaction kinetics and preparation of ferroelectric strontium bismuth niobate with a layered perovskite structure

2004 ◽  
Vol 19 (10) ◽  
pp. 2956-2963 ◽  
Author(s):  
Chung-Hsin Lu ◽  
Wei-Tse Hsu ◽  
Jiun-Ting Lee
Keyword(s):  
Reaction Kinetics ◽  
Formation Mechanism ◽  
Integral Method ◽  
Correlation Coefficients ◽  
Differential Method ◽  
Layered Perovskite ◽  
Heating Rates ◽  
Integral Methods ◽  
Diffusion Controlled ◽  
Layered Perovskite Structure

Ferroelectric layered perovskite SrBi2Nb2O9 has been successfully prepared through a new process using BiNbO4 as a precursor. The SrBi2Nb2O9 formation mechanism was investigated using a nonisothermal analysis method at constant heating rates. The weight loss recorded in thermal analysis under different heating rates was analogized to the reaction conversion. A combination of the differential and integral methods was introduced to solve the reaction mechanisms. Analysis using the differential method revealed that two kinds of diffusion-controlled models have higher linear correlation coefficients than other models. Based on the integral method principle, a new integral equation combining the Arrhenius equation and the Lobatto approximation was derived in this study. The established equation significantly simplified the conventional calculation process and improved the accuracy for predicting the reaction models. Analysis using the integral method corroborated that the SrBi2Nb2O9 formation mechanism is governed by Jander's diffusion controlled model, and the activation energy was calculated to be 192.1 kJ/mol. The proposed methods and the derived equations can be further applied to other solid-state-reaction systems to elucidate their reaction kinetics and estimate the related kinetic parameters.

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Mario Di Paola ◽  
Gioacchino Alotta
Keyword(s):  
Path Integral ◽  
Path Integration ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Kolmogorov Equation ◽  
Integral Methods ◽  
Alternative Approach ◽  
Path Integration Method ◽  
Path Integral Method ◽  
Barrier Problems

Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is analyzed. Lastly, an alternative approach to the path integration method, that is the Wiener Path integration (WPI), also based on the Chapman–Komogorov equation, is discussed. The main advantages and the drawbacks in using these two methods are deeply analyzed and the main results available in literature are highlighted.

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