A generalized $(G'/G)$-expansion method for the loaded Korteweg—de Vries equation

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

doi:10.33048/sibjim.2021.24.410

Cited by 8 publications

(3 citation statements)

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“…The (G /G) -expansion method was used to integrate the loaded Kortewegde Vries (KdV) equation and the loaded modified Korteweg-de Vries (mKdV) equation in [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Integration of the Loaded Negative Order Korteweg-De Vries Equation in the Class of Periodic Functions

Urazboev,

Khasanov,

Ganjaev

2024

Int. J. of Appl. Math.

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In this paper, we consider the loaded Korteweg-de Vries equation of negative order in the class of periodic functions corresponding to the eigenvalues of the corresponding spectral problem. It is shown that the considered equation can be integrated by the method of the inverse spectral problem. The evolution of the spectral data of the Sturm-Liouville operator with a periodic potential associated with the solution of the considered equation is determined. The obtained results make it possible to apply the inverse problem method for solving the loaded Korteweg-de Vries equation of negative order in the class of periodic functions corresponding to the eigenvalues of the corresponding spectral problem.

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“…The (G /G) -expansion method was used to integrate the loaded Kortewegde Vries (KdV) equation and the loaded modified Korteweg-de Vries (mKdV) equation in [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Integration of the Loaded Negative Order Korteweg-De Vries Equation in the Class of Periodic Functions

Urazboev,

Khasanov,

Ganjaev

2024

Int. J. of Appl. Math.

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“…In [14,15,16,17], the term of "loaded equation" was used for the first time, the most general definitions of the loaded differential equation were given and also a detailed classifications of the differential loaded equations as well as their numerous applications were presented. A complete description of solutions of the nonlinear loaded equations and their applications can be found in papers [18,19,20,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Soliton Solutions of the Loaded Modified Calogero-Degasperis Equation

Babajanov¹,

Abdikarimov²

2022

Int. J. of Appl. Math.

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In this article, we construct exact travelling wave solutions of the loaded modified Calogero-Degasperis equation by (G ′ /G) -expansion method. The efficiency of this method for finding these exact solutions has been demonstrated. We establish several classes of explicit solutions -hyperbolic and trigonometric solutions containing free parameters. The solitary wave solutions of this equation follow from the traveling wave solutions for certain values of the parameters. All calculations have been made with the aid of Matlab program. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

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“…Among the works devoted to loaded equations, one should especially note the works of A. Kneser [31], L. Lichtenstein [32], A. M. Nakhushev [33], and others. A complete explanation of solutions of the nonlinear loaded PDEs and their uses can be found in papers [34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method

Abdikarimov¹

2022

Preprint

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In this paper, the functional variable method is used to establish solitary wave solutions and periodic wave solutions of the loaded quadratic non-linear Klein-Gordon equation, the loaded cubic non-linear Klein-Gordon equation and the loaded coupled non-linear Klein-Gordon equation. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab software. The main advantage of the proposed functional variable method over other methods is that it provides more new exact traveling wave solutions along with additional free parameters. The graphical representations of the soliton solutions and the periodic wave solutions by using distinct values of random parameter are demonstrated to better understand their physical features. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena.

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A generalized $(G'/G)$-expansion method for the loaded Korteweg—de Vries equation

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Cited by 8 publications

References 0 publications

Integration of the Loaded Negative Order Korteweg-De Vries Equation in the Class of Periodic Functions

Integration of the Loaded Negative Order Korteweg-De Vries Equation in the Class of Periodic Functions

Soliton Solutions of the Loaded Modified Calogero-Degasperis Equation

Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method

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