A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation

With the aid of symbolic computation, a new extended Jacobi elliptic function expansion method is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi elliptic functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi elliptic function solutions of nonlinear partial differential equations. As an application of the method, we choose the generalized shallow water wave (GSWW) equation to illustrate the method. As a result, we can successfully obtain more new solutions. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.

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Construction of periodic and solitary wave solutions by the extended Jacobi elliptic function expansion method

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2006.01.013 ◽

2007 ◽

Vol 12 (7) ◽

pp. 1229-1241 ◽

Cited By ~ 55

Author(s):

M.A. Abdou ◽

A. Elhanbaly

Keyword(s):

Solitary Wave ◽

Elliptic Function ◽

Expansion Method ◽

Jacobi Elliptic Function ◽

Solitary Wave Solutions ◽

Wave Solutions ◽

Function Expansion ◽

Jacobi Elliptic Function Expansion

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Extended Jacobi Elliptic Function Expansion Method to the ZK-MEW Equation

International Journal of Differential Equations ◽

10.1155/2011/451420 ◽

2011 ◽

Vol 2011 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Weimin Zhang

Keyword(s):

Solitary Wave ◽

Elliptic Function ◽

Expansion Method ◽

Periodic Wave ◽

Jacobi Elliptic Function ◽

Solitary Wave Solutions ◽

Periodic Wave Solutions ◽

Wave Solutions ◽

Function Expansion ◽

Jacobi Elliptic Function Expansion

The extended Jacobi elliptic function expansion method is applied for Zakharov-Kuznetsov-modified equal-width (ZK-MEW) equation. With the aid of symbolic computation, we construct some new Jacobi elliptic doubly periodic wave solutions and the corresponding solitary wave solutions and triangular functional (singly periodic) solutions.

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Solitary and traveling wave solutions for the Davey–Stewartson equation using the Jacobi elliptic function expansion method

Optical and Quantum Electronics ◽

10.1007/s11082-020-02385-7 ◽

2020 ◽

Vol 52 (6) ◽

Author(s):

Nikola Zoran Petrović

Keyword(s):

Elliptic Function ◽

Traveling Wave ◽

Traveling Wave Solutions ◽

Expansion Method ◽

Jacobi Elliptic Function ◽

Wave Solutions ◽

Function Expansion ◽

Jacobi Elliptic Function Expansion

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Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

Contemporary Mathematics ◽

10.37256/cm.232021682 ◽

2021 ◽

pp. 173-188

Author(s):

Zillur Rahman ◽

M. Zulfikar Ali ◽

Harun-Or-Roshid ◽

Mohammad Safi Ullah

Keyword(s):

Elliptic Function ◽

Nonlinear Models ◽

Applied Mathematics ◽

Elliptic Functions ◽

Expansion Method ◽

Space Time ◽

Jacobi Elliptic Function ◽

Function Expansion ◽

Partial Models ◽

Jacobi Elliptic Function Expansion

In this manuscript, the space-time fractional Equal-width (s-tfEW) and the space-time fractional Wazwaz-Benjamin-Bona-Mahony (s-tfWBBM) models have been investigated which are frequently arises in nonlinear optics, solid states, fluid mechanics and shallow water. Jacobi elliptic function expansion integral technique has been used to build more innovative exact solutions of the s-tfEW and s-tfWBBM nonlinear partial models. In this research, fractional beta-derivatives are applied to convert the partial models to ordinary models. Several types of solutions have been derived for the models and performed some new solitary wave phenomena. The derived solutions have been presented in the form of Jacobi elliptic functions initially. Persevering different conditions on a parameter, we have achieved hyperbolic and trigonometric functions solutions from the Jacobi elliptic function solutions. Besides the scientific derivation of the analytical findings, the results have been illustrated graphically for clear identification of the dynamical properties. It is noticeable that the integral scheme is simplest, conventional and convenient in handling many nonlinear models arising in applied mathematics and the applied physics to derive diverse structural precise solutions.

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A variety of exact analytical solutions of extended shallow water wave equations via improved (G’/G) -expansion method

International Journal of Physical Research ◽

10.14419/ijpr.v5i1.7429 ◽

2017 ◽

Vol 5 (1) ◽

pp. 21 ◽

Cited By ~ 4

Author(s):

Faisal Hawlader ◽

Dipankar Kumar

Keyword(s):

Shallow Water ◽

Traveling Wave ◽

Water Wave ◽

Wave Equations ◽

Rational Functions ◽

Expansion Method ◽

Arbitrary Parameter ◽

Shallow Water Wave ◽

Wave Solutions ◽

Shallow Water Wave Equations

In this present work, we have established exact solutions for (2+1) and (3+1) dimensional extended shallow-water wave equations in-volving parameters by applying the improved (G’/G) -expansion method. Abundant traveling wave solutions with arbitrary parameter are successfully obtained by this method, and these wave solutions are expressed in terms of hyperbolic, trigonometric, and rational functions. The improved (G’/G) -expansion method is simple and powerful mathematical technique for constructing traveling wave, solitary wave, and periodic wave solutions of the nonlinear evaluation equations which arise from application in engineering and any other applied sciences. We also present the 3D graphical description of the obtained solutions for different cases with the aid of MAPLE 17.

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