New Solutions of Gardner's Equation Using Two Analytical Methods

@article{Ghanbari2019NewSO,
  title={New Solutions of Gardner's Equation Using Two Analytical Methods},
  author={Behzad Ghanbari and Dumitru Baleanu},
  journal={Frontiers in Physics},
  year={2019},
  volume={7},
  pages={202}
}
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… 

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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
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
Extension of the Exp-function method for systems of two-dimensional Burgers equations
Nonlocal symmetries and explicit solutions for the Gardner equation
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
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
TLDR
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.
Nonlocal symmetry and exact solutions of the (2+1)-dimensional Gardner equation
On Lie symmetries and invariant solutions of (2+1)-dimensional Gardner equation
Exact solutions for a compound KdV-Burgers equation
...
...