The modified simple equation method for solving nonlinear diffusive predator-prey system and Bogoyavlenskii equations
Elsayed M.E. Zayed,Y. A. Amer +1 more
TL;DR: The modified simple equation method (The modified SEM) was employed to find the exact traveling wave solutions involving parameters for two nonlinear evolution equations, namely, the diffusive predator-prey system and the Bogoyavlenskii equations as mentioned in this paper.
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Abstract: The modified simple equation method (The modified SEM) is employed to find the exact traveling wave solutions involving parameters for two nonlinear evolution equations, namely, the diffusive predator-prey system and the Bogoyavlenskii equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified SEM provides an effective and a more powerful mathematical tool for solving nonlinear partial differential equations in mathematical physics. Our results in this paper are new and different from those obtained in the literature.
Key words: A diffusive predator-prey system, the Bogoyavlenskii equation, the modified SEM, traveling wave solutions, solitary wave solutions.
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Citations
An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system
Md. Nur Alam,Cemil Tunç +1 more
TL;DR: In this paper, the exp ( - Φ ( ξ ) -expansion method was applied to construct many families of exact solutions of nonlinear evolution equations (NLEEs) via the nonlinear diffusive predator-prey system and the Bogoyavlenskii equations.
53
The effect of Brownian motion and noise strength on solutions of stochastic Bogoyavlenskii model alongside conformable fractional derivative
TL;DR: In this paper , the authors obtained wave solutions of fractional order stochastic Bogoyavlenskii equation (SBE) in the viewpoint of stratonovich regarding multiplicative noise.
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Perturbed Gerdjikov–Ivanov equation: Soliton solutions via Backlund transformation
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TL;DR: This study applies the Riccati-Bernoulli sub-ODE method and Backlund transformation to the perturbed Gerdjikov-Ivanov equation, yielding soliton solutions, trigonometric functions, and rational expressions, and providing a novel approach to nonlinear models in optical fibres.
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Highly dispersive optical solitons in the nonlinear Schrödinger’s equation having polynomial law of the refractive index change
Elsayed M.E. Zayed,Mohamed E.M. Alngar,Mahmoud M. El-Horbaty,Anjan Biswas,Mehmet Ekici,Qin Zhou,Salam Khan,Fouad Mallawi,Milivoj R. Belic +8 more
TL;DR: In this article, the authors apply the unified Riccati equation expansion method, as well as two forms of auxiliary equation methodology, to find highly dispersive optical solitons in the nonlinear Schrodinger's equation having a polynomial law of the refractive index change.
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Explicit and Approximate Solutions for the Conformable-Caputo Time-Fractional Diffusive Predator–Prey Model
TL;DR: In this paper, a conformable-time fractional predator-prey model was proposed by adapting the extended Kudryashov method and a fractional power series solution was found for the same model when the fractional derivative is of Caputo type.
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References
Extended tanh-function method and its applications to nonlinear equations
TL;DR: In this article, an extended tanh-function method is proposed for constructing multiple travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way, and the key idea of this method is to take full advantage of a Riccati equation involving a parameter and use its solutions to replace the tanh function.
2K
Exp-function method for nonlinear wave equations
Ji-Huan He,Xu-Hong Wu +1 more
TL;DR: In this article, a new method, called Exp-function method, is proposed to seek solitary solutions, periodic solutions and compacton-like solutions of nonlinear differential equations, and the modified KdV equation and Dodd-Bullough-Mikhailov equation are chosen to illustrate the effectiveness and convenience of the suggested method.
2K
The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
TL;DR: The (G'/G)-expansion method is firstly proposed in this paper, where G = G(xi) satisfies a second order linear ordinary differential equation (LODE for short), by which the travelling wave solutions involving parameters of the KdV equation, the mKdV equations, the variant Boussinesq equations and the Hirota-Satsuma equations are obtained when the parameters are taken as special values.
1.9K
Solitary wave solutions of nonlinear wave equations
TL;DR: In this article, a method for obtaining traveling-wave solutions of nonlinear wave equations that are essentially of a localized nature is proposed based on the fact that most solutions are functions of a hyperbolic tangent.
1.5K
Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
TL;DR: In this article, a Jacobi elliptic function expansion method was proposed to construct the exact periodic solutions of nonlinear wave equations, which includes some shock wave solutions and solitary wave solutions.
1.4K