New Solutions of Gardner's Equation Using Two Analytical Methods

@article{Ghanbari2019NewSO,
title={New Solutions of Gardner's Equation Using Two Analytical Methods},
journal={Frontiers in Physics},
year={2019},
volume={7},
pages={202}
}
• Published 6 December 2019
• Physics
• Frontiers in Physics
me exact solutions to the Gardner’s equation are obtained with the help of two analytical methods including the generalized exponential rational function method and a Jacobi elliptical solution finder method. A set of new exact solutions containing four parameters is reported. The graphical interpretation of the solutions is depicted. Mathematica software is used to perform the computations and simulations. The suggested techniques can be used to another sort of real-world models from science…
25 Citations

Figures and Tables from this paper

Some new families of exact solutions to a new extension of nonlinear Schrödinger equation
• Mathematics
Physica Scripta
• 2020
Determining the exact solution to the partial differential equations has been one of the most important concerns of scientists in the various centuries. This paper applies the generalized exponential
Exact Traveling Wave Solutions of the Gardner Equation by the Improved tanΘϑ-Expansion Method and the Wave Ansatz Method
Nonlinear partial differential equations (NLPDEs) are an inevitable mathematical tool to explore a large variety of engineering and physical phenomena. Due to this importance, many mathematical
On novel nondifferentiable exact solutions to local fractional Gardner's equation using an effective technique
• B. Ghanbari
• Mathematics
Mathematical Methods in the Applied Sciences
• 2020
One of the most interesting branches of fractional calculus is the local fractional calculus, which has been used successfully to describe many fractal problems in science and engineering. The main
On abundant new solutions of two fractional complex models
• Mathematics
• 2020
We use an analytical scheme to construct distinct novel solutions of two well-known fractional complex models (the fractional Korteweg–de Vries equation (KdV) equation and the fractional
A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order
• Mathematics
• 2020
We investigate some solitary wave results of time fractional evolution equations. By employing the extended rational exp ( ( − ψ ′ ψ ) ( η ) ) $\exp ( (-\frac{{\psi }^{\prime }}{\psi }) ( \eta ) )$
Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients
• Mathematics
Symmetry
• 2021
In this paper, we employ the certain theory of Lie symmetry analysis to discuss the time-fractional Gardner equation with time-dependent coefficients. The Lie point symmetry is applied to realize the

References

SHOWING 1-10 OF 37 REFERENCES
A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation
• Mathematics, Physics
• 2018
Abstract.The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational
A New Approach for the Exact Solutions of Nonlinear Equations of Fractional Order via Modified Simple Equation Method
In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the
A study of shallow water waves with Gardner’s equation
• Mathematics
• 2011
In this paper the dynamics of solitary waves governed by Gardner’s equation for shallow water waves is studied. The mapping method is employed to carry out the integration of the equation.
Traveling Wave Analysis of Partial Differential Equations: Numerical and Analytical Methods with Matlab and Maple
• Computer Science
• 2011
The authors' intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs.