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

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.

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

Revista Mexicana de Física ◽

10.31349/revmexfis.65.73 ◽

2018 ◽

Vol 65 (1) ◽

pp. 73 ◽

Cited By ~ 6

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.

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Application of the extension exponential rational function method for higher-dimensional Broer–Kaup–Kupershmidt dynamical system

Modern Physics Letters A ◽

10.1142/s0217732319503450 ◽

2019 ◽

Vol 35 (01) ◽

pp. 1950345 ◽

Cited By ~ 4

Author(s):

Aly R. Seadawy ◽

K. El-Rashidy

Keyword(s):

Dynamical System ◽

Mathematical Method ◽

Partial Differential Equations ◽

Exact Solutions ◽

Rational Function ◽

Function Method ◽

Nonlinear Partial Differential Equations ◽

Exponential Functions ◽

Higher Dimensional ◽

Exponential Rational Function Method

The extension of exponential rational function method is obtained to construct a series of exact solutions for higher-dimensional Broer–Kaup–Kupershmidt (BKK) dynamical system. New and general solutions are found. The solutions reported in this work are kink solutions, anti-kink solutions and bright solutions. They are expressed in terms of rational exponential functions. A confrontation of our results with the well-known results are done and it comes from this study that the solutions obtained here are new. The mathematical method applied to search for our solutions can be used for other nonlinear partial differential equations. The graphics of the obtained solutions in this paper are shown.

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Abundant exact solutions to the strain wave equation in micro-structured solids

Modern Physics Letters B ◽

10.1142/s021798492150439x ◽

2021 ◽

pp. 2150439

Author(s):

Karmina K. Ali ◽

R. Yilmazer ◽

H. Bulut ◽

Tolga Aktürk ◽

M. S. Osman

Keyword(s):

Wave Propagation ◽

Wave Equation ◽

Exact Solutions ◽

Rational Function ◽

Physical Interpretation ◽

Function Method ◽

Nonlinear Partial Differential Equations ◽

Singular Solutions ◽

Strain Wave ◽

Important Place

In this study, the strain wave equation in micro-structured solids which take an important place in solid physics is presented for consideration. The generalized exponential rational function method is used for this purpose which is one of the most powerful methods of constructing abundantly distinct, exact solutions of nonlinear partial differential equations. In micro-structured solids, wave propagation is based on the structure of the strain wave equation. As a consequence, we successfully received many different exact solutions, including non-topological solutions, periodic singular solutions, topological solutions, singular solutions, like periodic lump solutions. Furthermore, in order to better understand their physical interpretation, 2D, 3D, and counter plots are graphed for each of the solutions acquired.

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Application of the Exponential Rational Function Method to Some Fractional Soliton Equations

Emerging Applications of Differential Equations and Game Theory - Advances in Computer and Electrical Engineering ◽

10.4018/978-1-7998-0134-4.ch002 ◽

2020 ◽

pp. 13-32

Author(s):

Mustafa Ekici ◽

Metin Ünal

Keyword(s):

Differential Equations ◽

Rational Function ◽

Function Method ◽

Space Time ◽

Fractional Equations ◽

New Exact Solutions ◽

Kdv Equations ◽

Fractional Differential ◽

Exponential Rational Function Method ◽

Fifth Order

In this chapter, the authors study the exponential rational function method to find new exact solutions for the time-fractional fifth-order Sawada-Kotera equation, the space-time fractional Whitham-Broer-Kaup equations, and the space-time fractional generalized Hirota-Satsuma coupled KdV equations. These fractional differential equations are converted into ordinary differential equations by using the fractional complex transform. The fractional derivatives are defined in the sense of Jumarie's modified Riemann-Liouville. The proposed method is direct and effective for solving different kind of nonlinear fractional equations in mathematical physics.

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

Modern Physics Letters B ◽

10.1142/s0217984919504025 ◽

2019 ◽

Vol 33 (32) ◽

pp. 1950402 ◽

Cited By ~ 5

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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Abundant soliton solutions for the Hirota–Maccari equation via the generalized exponential rational function method

Modern Physics Letters B ◽

10.1142/s0217984919501069 ◽

2019 ◽

Vol 33 (09) ◽

pp. 1950106 ◽

Cited By ~ 11

Author(s):

Behzad Ghanbari

Keyword(s):

Exact Solutions ◽

Rational Function ◽

Traveling Wave ◽

Function Method ◽

Soliton Solutions ◽

Traveling Wave Solutions ◽

Graphical Interpretation ◽

Wave Solutions ◽

Complex Models ◽

Exponential Rational Function Method

In this paper, some new traveling wave solutions to the Hirota–Maccari equation are constructed with the help of the newly introduced method called generalized exponential rational function method. Several families of exact solutions are found corresponding to the equation. To the best of our knowledge, these solutions are new, and have never been addressed in the literature. The graphical interpretation of the solutions is also depicted. Moreover, it is contemplated that the proposed technique can also be employed to another sort of complex models.

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