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56 articles for “Exact Solution”
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Research ArticleOpen accessPhrase in the titleApplication of an Enhanced (G'/G)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Particle PhysicsS.M. Rayhanul IslamThe enhanced (G'/G)-expansion method is very effective and powerful method to find the exact traveling wave solutions of nonlinear evolution equations. We choose the Phi-4 equation to illustrate the validity and advantages of this method. As a result, many exact traveling wave solutions are obtained, which include soliton, hyperbolic function and trigonometric function solutions. …American Journal of Applied Sciences, Vol. 12, Issue 11 · 13 Nov 2015 · 7,037 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleExact Solutions of Mass Transfer over a Stretching Surface with Chemical Reaction and Suction/InjectionHassan A.M. El-ArabawyProblem statement: In this research the researchers studied and made an analysis to the effects of suction/injection and chemical reaction on mass transfer characteristics over a stretching surface. The researcher studied the effects of some parameters appear on mass transfer. Approach: Transforming the system of partial differential equations to a system of ordinary differential equations and obtaining the exact analytical … …Journal of Mathematics and Statistics, Vol. 5, Issue 3 · 30 Sep 2009 · 7,510 accessesView PDFCite
Research ArticleOpen accessPhrase in the titleExact Solution of a Test Particle in Presence of Thick Domain WallsA. Al-BadawiWe have obtained the exact solution of the equations of motion of a test particle near a thick domain walls for the case of Ricci tensor Rab = 0. From the solution it has been shown that the domain walls have repulsive gravitational fields. …American Journal of Applied Sciences, Vol. 3, Issue 7 · 31 Jul 2006 · 6,235 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleFlow of Temperature-dependent Viscous Fluid Between Parallel Heated Walls: Exact Analytical Solutions in the Presence of Viscous DissipationK. S. Adegbie, F. I. AlaoWe examine steady incompressible flow of viscous liquids between parallel heated walls of plane Couette device. The temperature of the upper and lower walls of the device are maintained at T = Tb and T = T0 respectively. Of a particular interest are exact analytical solutions of the coupled non-linear differential equations resulting from plane Couette flow obtained for the … …Journal of Mathematics and Statistics, Vol. 3, Issue 1 · 31 Mar 2007 · 7,480 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleTheory of Exact Trigonometric Periodic Solutions to Quadratic Liénard Type EquationsJean Akande, Damien Kolawolé Kêgnidé Adjaï, Marc Delphin MonsiaA mathematical theory is developed through generalized Sundman transformation to show the existence of classes of quadratic Liénard type equations which admit exact and explicit general trigonometric solutions but with amplitude-dependent frequency. The application of the theory to compute also exact and explicit general periodic solutions to nonlinear differential equations like inverted Painlevé-Gambier equations in terms of trigonometric or Jacobian … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 29 Oct 2018 · 7,215 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleNew Family of Exact Soliton Solutions for the Nonlinear Three-Wave Interaction EquationsSahar M. Alqaraleh, Adeeb G. TalafhaProblem statement: To obtain new exact traveling wave soliton solutions for the threewave interaction equation in a dispersive medium and a non zero phase mismatch. Approach: The tanh method is usually used to find a traveling wave analytic soliton solutions for one nonlinear wave and evolution partial differential equation. Here, we generalize this method to solve a system of nonlinear … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 31 Jan 2011 · 7,426 accessesView PDFCite
Research ArticleOpen accessIn the keywordsSolutions of the Duffing and Painlevé-Gambier Equations by Generalized Sundman TransformationDamien Kolawolé Kêgnidé Adjaï, Lucas Hervé Koudahoun, Jean Akande et al.A new approach using the generalized Sundman transformation to solve explicitly and exactly in a straightforward manner the cubic elliptic Duffing equation is proposed in this study. The method has the advantage to closely relate this equation to the linear harmonic oscillator equation and to be applied to solve other nonlinear differential equations. As a result, explicit and exact general … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 8 Nov 2018 · 7,251 accessesView PDFCite
Research ArticleOpen accessIn the keywordsAnalytical Solutions of Riccati Fractional Equation with Coefficients Satisfying Differential Conditions with Arbitrary FunctionKhaled K. JaberNew exact solutions of the Fractional Riccati Differential equation are presented. Exact solutions are obtained in cases that the coefficient functions and an arbitrary function satisfy some differential conditions. In view of the conditions imposed on Riccati equation's coefficients we define and formulate the coefficients of the Riccati equation to obtain the differential cases, for each case the general solution … …Journal of Mathematics and Statistics, Vol. 13, Issue 4 · 27 Dec 2017 · 7,211 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn the Closed Form Solutions of Linear and Nonlinear Cauchy Reaction-Diffusion Equations Using the Hybrid of Fourier Transform and Variational Iteration MethodS.S. Nourazar, A. Nazari-Golshan, M. NourazarProblem statement: In the present study, a hybrid of Fourier transform and Variational Iteration Method (FTVIM) is developed for solving the non-homogeneous linear and nonlinear partial differential equations of Cauchy reaction-diffusion problem. Approach: The closed form solutions obtained from the series solution of recursive sequences is valid for the entire range of problem domain. Results and Conclusion: Moreover, the very … …Physics International, Vol. 2, Issue 1 · 26 Oct 2011 · 8,195 accessesView PDFCite
Research ArticleOpen accessIn the keywordsDetermination of Nonlinear Optimal Feedback Law for Satellite Injection Problem Using Neighboring Optimal ControlHamed Hossein Afshari, Alireza Basohbat Novinzadeh, Jafar RoshanianAn optimal trajectory design of a nonlinear satellite injection problem for transfer to a final target orbit by minimizing the time was investigated. Indeed, this design was an exact solution to the nonlinear two-point boundary value problem which determined optimal control history as well as optimal state trajectories in the open-loop form. Furthermore, the obtained optimal guidance strategy was exerted … …American Journal of Applied Sciences, Vol. 6, Issue 3 · 31 Mar 2009 · 7,256 accessesView PDFCite