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The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics
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Using the Painleve property, the traveling wave transformation, and the sine-Gordon expansion method (SGEM), a series of traveling wave solutions for the Tzitzeica type equations were obtained in this article.About:
This article is published in Optik.The article was published on 2017-11-01. It has received 122 citations till now. The article focuses on the topics: Nonlinear optics.read more
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Optical soliton perturbation with Fokas-Lenells equation using three exotic and efficient integration schemes
Anjan Biswas,Anjan Biswas,Anjan Biswas,Hadi Rezazadeh,Mohammad Mirzazadeh,Mostafa Eslami,Mehmet Ekici,Qin Zhou,Seithuti P. Moshokoa,Milivoj R. Belic +9 more
TL;DR: In this paper, the soliton dynamics in optical fibers with Fokas-Lenells equation is illustrated and the existence criteria of these solitons are also presented, along with few forms of combo-soliton solutions that naturally emerged from the three integration schemes applied to the model.
Journal ArticleDOI
Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method
TL;DR: In this paper, a modified auxiliary equation method was applied to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters, which is one of the fractional nonlinear partial differential equations.
Journal ArticleDOI
The system of equations for the ion sound and Langmuir waves and its new exact solutions
TL;DR: In this article, the system of equations for the ion sound and Langmuir waves (SEISLWs) was studied, and different integration schemes, including the modified Kudraysov method (MKM) and the hyperbolic function method (HFM), were used to acquire new exact solutions of the governing system.
Journal ArticleDOI
New explicit exact solutions of the unstable nonlinear Schrödinger’s equation using the exp a and hyperbolic function methods
TL;DR: In this paper, the unstable nonlinear Schrodinger's equation is studied, which points out the time evolution of disturbances in marginally stable or unstable media and a wide variety of new explicit exact solutions are successfully derived, proving the excellent performance of the schemes.
Journal ArticleDOI
New closed form soliton and other solutions of the Kundu-Eckhaus equation via the extended sinh-Gordon equation expansion method
TL;DR: In this paper, the extended sinh-Gordon equation expansion method (ShGEEM) was applied to look for new complex hyperbolic and complex trigonometric function solutions, especially dark, bright, combined dark-bright, singular, combined singular soliton and other soliton solutions.
References
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Journal ArticleDOI
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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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.
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The tan h method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations
TL;DR: In this article, the tan-h method is applied to the Dodd-Bullough-Mikhailov and Tzitzeica-Dodd-bullough equations and periodic solutions for these equations are formally derived.
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New exact solutions of Burgers’ type equations with conformable derivative
TL;DR: In this paper, the exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative of the Burgers-Korteweg-de Vries equation.
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New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method
Kamyar Hosseini,Reza Ansari +1 more
TL;DR: In this paper, the modified Kudryashov method was used to derive exact solutions for nonlinear Boussinesq equations with conformable time-fractional derivative.