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On the new soliton and optical wave structures to some nonlinear evolution equations
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TLDR
In this article, with the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is utilized to search for the solutions to some important nonlinear mathematical models arising in nonlinear sciences, namely, the (2 + 1) -dimensional Zakharov-Kuznetsov modified equal width equation, the cubic Boussinesq equation and the modified regularized long wave equation.Abstract:
In this study, with the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is utilized to search for the solutions to some important nonlinear mathematical models arising in nonlinear sciences, namely, the (2 + 1) -dimensional Zakharov-Kuznetsov modified equal width equation, the cubic Boussinesq equation and the modified regularized long wave equation. We successfully obtain some new soliton, singular soliton, singular periodic waves and kink-type solutions with complex hyperbolic structures to these equations. We also present the two- and three-dimensional shapes of all the solutions obtained in this study. We further give the physical meaning of all the obtained solutions. We compare our results with the existing results in the literature.read more
Citations
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On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel’d-Sokolov systems
TL;DR: In this article, the authors investigated the Nizhnik-Novikov-Veselov and the Drinfel-d-Sokolov systems by using the extended sinh-Gordon equation expansion method.
Journal ArticleDOI
Dark, bright and other soliton solutions to the Heisenberg ferromagnetic spin chain equation
TL;DR: In this paper, the applications of the extended sinh-Gordon equation expansion method to a nonlinear Schrodinger equation that describes the nonlinear spin dynamics of (2 + 1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit is presented.
Journal ArticleDOI
On the bright and singular optical solitons to the ( $$2+1$$ 2 + 1 )-dimensional NLS and the Hirota equations
TL;DR: In this paper, the authors constructed bright and singular optical solitons for the (€ 2+1$$ )-dimensional NLSE and the Hirota equation by utilizing the new sine-Gordon expansion method.
Journal ArticleDOI
Optical solitons and other solutions to the conformable space-time fractional complex Ginzburg-Landau equation under Kerr law nonlinearity
TL;DR: In this article, the authors reveal the dark, bright, combined dark-bright, singular, combined singular optical solitons and singular periodic solutions to the conformable space-time fractional complex Ginzburg-Landau equation.
Journal ArticleDOI
A new rational sine-Gordon expansion method and its application to nonlinear wave equations arising in mathematical physics
TL;DR: In this article, a generalization of the sine-Gordon expansion method is proposed to construct exact solutions to nonlinear partial differential equations (PDE), which is based on the use of the SING equation as an auxiliary equation.
References
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Journal ArticleDOI
Calculations of the development of an undular bore
TL;DR: In this paper, the growth of an undular bore from a long wave is described, which forms a gentle transition between a uniform flow and still water, and a physical account of its development is followed by the results of numerical calculations.
Journal ArticleDOI
A simple transformation for nonlinear waves
TL;DR: In this article, a transformation method is proposed to establish a relation between linear and nonlinear wave theories, which can be obtained from the sine-Gordon equation and is simpler than the hyperbolic tangent method in solving differential equations.
Journal ArticleDOI
A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation
Wen-Xiu Ma,Jyh-Hao Lee +1 more
TL;DR: In this article, a direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations, which provides a more systematical and convenient handling of the solution process of non-linear equations, unifying the tanh-function type methods, the homogeneous balance method, the exp-function method, and the mapping method.
Journal ArticleDOI
A multiple exp-function method for nonlinear differential equations and its application
TL;DR: In this article, a multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed, which is oriented towards ease of use and capability of computer algebra systems.
Journal ArticleDOI
A multiple exp-function method for nonlinear differential equations and its application
TL;DR: In this paper, a multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed, oriented towards the ease of use and capability of computer algebra systems.
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