The Generalized $$(G^{\prime }/G) $$-Expansion Method for the Loaded Korteweg–de Vries Equation

Urazboev, G. U.; Baltaeva, I. I.; Rakhimov, I.D.

doi:10.1134/s1990478921040116

Cited by 5 publications

(2 citation statements)

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“…where 19) is a solution of equation ( 9), provided that the integration constant C in equation ( 9) is taken as that in (18). Substituting the general solutions of equation ( 11) into (19), we obtain three types of travelling wave solutions of the loaded Burgers equation ( 1) as follows:…”

Section: Exact Solution Of the Loaded Burgers Equationmentioning

confidence: 99%

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Generalized (G'/G) - Expansion Method and its Applications to the Loaded Burgers Equation

Urazboev¹,

Хасанов²,

Rakhimov³

2023

Az. J. Math.

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This paper is dedicated to finding the traveling wave solutions of the loaded Burgers equation. We show how to find the solutions via the (G ′ /G) -expansion method which is one of the most effective ways of finding solutions. When the parameters are taken as special values, the solitary waves are also derived from the traveling waves. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. This method is easy to implement using well-known software packages, which allows you to solve complex nonlinear evolution equations of mathematical physics.

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Section: Exact Solution Of the Loaded Burgers Equationmentioning

confidence: 99%

“…Integration of the loaded modified Korteweg-de Vries (mKdV) equation in the class of periodic functions was treated in [18]. (G ′ /G) -expansion method was used for the integrations of loaded Korteweg-de Vries (KdV) equation and the loaded modified Korteweg-de Vries (mKdV) equation in [19,20].…”

Section: Introductionmentioning

confidence: 99%