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

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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Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽

10.2298/fil1809347k ◽

2018 ◽

Vol 32 (9) ◽

pp. 3347-3354 ◽

Cited By ~ 1

Author(s):

Nematollah Kadkhoda ◽

Michal Feckan ◽

Yasser Khalili

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Exact Solutions ◽

Present Article ◽

Analytical Solutions ◽

Nonlinear Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Rational Functions ◽

Expansion Method ◽

Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

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New Exact Solutions for Two Nonlinear Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-2006-1-201 ◽

2006 ◽

Vol 61 (1-2) ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Zonghang Yang

Keyword(s):

Wave Equation ◽

Partial Differential Equations ◽

Exact Solutions ◽

Water Wave ◽

Function Method ◽

Nonlinear Partial Differential Equations ◽

Soliton Solutions ◽

New Exact Solutions ◽

Complex Phenomena ◽

Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

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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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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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Exact solutions of the unstable nonlinear Schrödinger equation with the new Jacobi elliptic function rational expansion method and the exponential rational function method

Optik ◽

10.1016/j.ijleo.2016.08.116 ◽

2016 ◽

Vol 127 (23) ◽

pp. 11124-11130 ◽

Cited By ~ 26

Author(s):

E. Tala-Tebue ◽

Z.I. Djoufack ◽

E. Fendzi-Donfack ◽

A. Kenfack-Jiotsa ◽

T.C. Kofané

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Rational Function ◽

Elliptic Function ◽

Schrodinger Equation ◽

Function Method ◽

Expansion Method ◽

Nonlinear Schrodinger Equation ◽

Jacobi Elliptic Function ◽

Exponential Rational Function Method

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

Modern Physics Letters B ◽

10.1142/s0217984919500611 ◽

2019 ◽

Vol 33 (06) ◽

pp. 1950061 ◽

Cited By ~ 8

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.

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