scholarly journals Optical soliton solutions of the Ginzburg-Landau equation with conformable conformable derivative and Kerr law nonlinearity

2018 ◽  
Vol 65 (1) ◽  
pp. 73 ◽  
Author(s):  
Francisco Gomez ◽  
Behzad Ghanbari
Keyword(s):  
Rational Function ◽  
Function Method ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Conformable Derivative ◽  
Ginzburg Landau ◽  
Kerr Law ◽  
Ginzburg Landau Equation ◽  
Kerr Law Nonlinearity ◽  
Exponential Rational Function Method

By using the generalized exponential rational function method we obtain new periodic and hyperbolic soliton solutions for the conformable Ginzburg-Landau equation with Kerr law nonlinearity. The conformable derivative was considered to obtain the exact solutions under constraint conditions. To determine the solution of the model, the method uses the generalization of the exponential rational function method. Numerical simulations are performed to confirm the efficiency of the proposed method.

Exact optical solitons of Radhakrishnan–Kundu–Lakshmanan equation with Kerr law nonlinearity

2019 ◽  
Vol 33 (06) ◽  
pp. 1950061 ◽  
Author(s):  
Behzad Ghanbari ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Mustafa Bayram
Keyword(s):  
Optical Fiber ◽  
Rational Function ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Kerr Nonlinearity ◽  
Optical Solitons ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Exponential Rational Function Method ◽  
Special Case

A new generalized exponential rational function method (GERFM) is used to acquire some new optical solitons of Radhakrishnan–Kundu–Lakshmanan (RKL) equation with Kerr nonlinearity. This equation is used to model propagation of solitons through an optical fiber. The well-known exponential rational function method is also a special case of the GERFM. The results reveal that the mentioned method is efficient and simple for solving different nonlinear partial differential equations.

scholarly journals Application of Modified Extended Tanh Technique for solving Complex Ginzburg-Landau Equation considering Kerr Law Nonlinearity

2021 ◽  
Vol 66 (2) ◽  
pp. 1369-1378
Author(s):  
Yu-Ming Chu ◽  
Muhannad A. Shallal ◽  
Seyed Mehdi Mirhosseini-Alizamini ◽  
Hadi Rezazadeh ◽  
Shumaila Javeed ◽  
...  
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
Kerr Law ◽  
Ginzburg Landau Equation ◽  
Kerr Law Nonlinearity

Combined multi-waves rational solutions for complex Ginzburg–Landau equation with Kerr law of nonlinearity

2019 ◽  
Vol 34 (03) ◽  
pp. 1950019 ◽  
Author(s):  
Iftikhar Ahmed ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Landau Equation ◽  
Rational Solution ◽  
Soliton Interaction ◽  
Rational Solutions ◽  
Ginzburg Landau ◽  
Interaction Solutions ◽  
Kerr Law ◽  
Ginzburg Landau Equation ◽  
Kink Wave ◽  
Waves Interaction

By utilizing the logarithmic transformation and symbolic computation with ansatz functions technique, rational solution and multi-waves interaction solutions are obtained for complex Ginzburg–Landau equation with Kerr law of nonlinearity. Meanwhile, the interaction between rational solutions and the kink wave is also investigated. The dynamics of these obtained solutions are analyzed and described in figures by selecting appropriate values of parameters. Through graphical interpretation, we observe the dynamics and characteristics of lump-kink interaction, soliton–soliton interaction, multi-waves interactions and breathers.

Optical soliton solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation

2019 ◽  
Vol 33 (32) ◽  
pp. 1950402 ◽  
Author(s):  
Behzad Ghanbari ◽  
J. F. Gómez-Aguilar
Keyword(s):  
Rational Function ◽  
Imaginary Part ◽  
Traveling Waves ◽  
Analytical Solutions ◽  
Efficient Method ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Complex Structures ◽  
Exponential Rational Function Method

In this paper, the generalized exponential rational function method is applied to obtain analytical solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation. We obtain novel soliton, traveling waves and kink-type solutions with complex structures. We also present the two- and three-dimensional shapes for the real and imaginary part of the solutions obtained. It is illustrated that generalized exponential rational function method (GERFM) is simple and efficient method to reach the various type of the soliton solutions.

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