Study of the Analytical Treatment of the (2+1)-Dimensional Zoomeron, the Duffing and the SRLW Equations via a New Analytical Approach
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In this paper, the authors applied the improved tan (ξ )/ 2-expansion scheme for the (2+1)-dimensional Zoomeron, the Duffing and the symmetric regularized long wave equa- tions andexactparticularsolutions have been found.Abstract:
In this paper, we applied the improved tan (�(ξ )/ 2)-expansion scheme for the (2+1)-dimensional Zoomeron, the Duffing and the symmetric regularized long wave equa- tionsandexactparticularsolutionshavebeenfound.Theexactparticularsolutionscontaining four types hyperbolic function solution, trigonometric function solution, exponential solu- tion and rational solution. We obtained the further solutions comparing with other methods as sine-cosine function method (Qawasmeh in J Math Comput Sci 3:1475-1480, 2013). Recently this method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that this method, with the help of symbolic com- putation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.read more
Citations
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An investigation of fractional complex Ginzburg–Landau equation with Kerr law nonlinearity in the sense of conformable, beta and M-truncated derivatives
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Exact Traveling Wave Solutions of the Gardner Equation by the Improved tanΘϑ-Expansion Method and the Wave Ansatz Method
Hatıra Günerhan,Hatıra Günerhan +1 more
TL;DR: In this paper, the exact bright, dark, singular, and W-shaped soliton solutions of the Gardner equation were derived via two well-known analytical approaches, namely, the improved -expansion method and the wave ansatz method.
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On the exact and numerical solutions to a new (2 + 1)-dimensional Korteweg-de Vries equation with conformable derivative
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Solitary Wave Solutions for $$(1+2)$$ ( 1 + 2 ) -Dimensional Nonlinear Schrödinger Equation with Dual Power Law Nonlinearity
Pallavi Verma,Lakhveer Kaur +1 more
TL;DR: In this article, the Schrodinger equation (NLSE) with dual power law nonlinearity was applied to find exact traveling wave solutions in terms of exponential functions, and various arbitrary constants obtained in the solutions help us to discuss the graphical behavior of solutions and also grant flexibility to form a link with large variety of physical phenomena.
References
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TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
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Variational iteration method – a kind of non-linear analytical technique: some examples
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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.
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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.
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