Results 1 to 10 of about 13,925,367 (271)

Trial equation method and its applications to nonlinear evolution equations

Acta Physica Sinica, 2005
A new method, that is, trial equation method, was given to obtain the exact trav eling wave solutions for nonlinear evolution equations. As an example, a class o f fifth-order nonlinear evolution equations was discussed. Its exact traveling w ave solutions, which included rational form solutions, solitary wave solutions, triangle function periodic ...
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On the Solution of Nonlinear Time-Fractional Generalized Burgers Equation by Homotopy Analysis Method and Modified Trial Equation Method [PDF]

International Journal of Modeling and Optimization, 2014
In this paper, we have executed the Homotopy Analysis Method and Modified Trial Equation Method which has newly been submitted to the literature for obtaining analytical solution of the nonlinear time-fractional generalized Burgers equation occuring in various areas of physics, chemistry, applied sciences, applied mathematics such as modeling of gas ...
Haci Mehmet Baskonus, Hasan Bulut, Yusuf Pandir   +2 more
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THE SOLUTION TO THE EQUATION OF THE SHOCK WAVE BURGERS IN THE PTC MATHCAD ENVIRONMENT

Современная наука и инновации, 2022
The system of equations of ordinary differential equations is integrated by means of the Euler computational scheme, and the step size is maintained small enough that the errors associated with numerical integration are negligible in comparison with the ...
R. E. Oleynikova
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Solitons in optical metamaterials with anti-cubic law of nonlinearity by ETEM and IGEM

Journal of the European Optical Society-Rapid Publications, 2018
Background This paper studies soliton perturbation in optical metamaterials, with anticubic nonlinearity. Methods Two integration approaches, namely, the extended trial equation method (ETEM) and the improved G’/Gexpansion method (IGEM) are presented ...
Mohammadreza Foroutan, Jalil Manafian, Arash Ranjbaran   +2 more
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Optimization of Trial Wave Function in Determining the Ground State Energy of Helium Atom

Jurnal Fisika, 2018
The atomic ground state properties of helium, especially with regard to the ground state energy, can be studied by using various methods. One such method is the variational method.
Yacobus Yulianto, Zaki Su'ud
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Simple Equations Method (SEsM): Algorithm, Connection with Hirota Method, Inverse Scattering Transform Method, and Several Other Methods

Entropy, 2020
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected ...
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov   +2 more
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Generalized trial equation method and its applications toDuffing and Poisson--Boltzmann equations

TURKISH JOURNAL OF MATHEMATICS, 2017
Summary: The trial equation method, which was proposed by Cheng-Shi Liu, is a very powerful method for solving nonlinear differential equations. After the original trial method, some modified versions of the trial equation method were introduced and applied to some famous nonlinear differential equations.
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Trigonometric Function Solutions of Fractional Drinfeld's Sokolov -Wilson System

ITM Web of Conferences, 2017
In this paper, we construct exact trigonometric solutions of the space-time fractional classical Drinfeld's Sokolov-Wilson system by Modified Trial Equation Method (MTEM).
Koçak Zeynep Fidan, Yel Gülnur
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Modified Trial Equation Method to the Nonlinear Fractional Sharma–Tasso–Olever Equation

International Journal of Modeling and Optimization, 2013
In this paper, we apply the modified trial equation method to fractional partial differential equations. The fractional partial differential equation can be converted into the nonlinear non-fractional ordinary differential equation by the fractional derivative and traveling wave transformation.
Hasan Bulut, Yusuf Pandir
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Qualitative analysis and optical solitons for the (1+1)-dimensional Biswas-Milovic equation with parabolic law and nonlocal nonlinearity

Results in Physics
In this paper, the (1+1)-dimensional Biswas-Milovic equation with parabolic law and nonlocal nonlinearity is studied. Firstly, the Biswas-Milovic equation with parabolic law and nonlocal nonlinearity is transformed into ordinary differential equation ...
Zhao Li, Ejaz Hussain
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