An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients
The extended generalized G′G–expansion is well defined and an efficient technique, which is used to obtain the exact traveling wave solutions to the governing nonlinear equations with constant coefficients as well as variable coefficients. In this paper, the modified Korteweg–de Vries (mKdV) equatio...
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| Language: | English |
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Elsevier
2022-06-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722002443 |
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| author | Sanjaya K. Mohanty Sachin Kumar Apul N. Dev Manoj Kr. Deka Dmitry V. Churikov Oleg V. Kravchenko |
| author_facet | Sanjaya K. Mohanty Sachin Kumar Apul N. Dev Manoj Kr. Deka Dmitry V. Churikov Oleg V. Kravchenko |
| author_sort | Sanjaya K. Mohanty |
| collection | DOAJ |
| description | The extended generalized G′G–expansion is well defined and an efficient technique, which is used to obtain the exact traveling wave solutions to the governing nonlinear equations with constant coefficients as well as variable coefficients. In this paper, the modified Korteweg–de Vries (mKdV) equation and Burgers equation with variable coefficients are investigated through the extended generalized G′G–expansion method, which are exceptional cases of the nonlinear evolution equations widely used in a two-layer fluid system, in fluid-filled elastic tubes, in an atmospheric and oceanic dynamical system, traffic flow, turbulence in fluid dynamics, dusty plasma, ion-acoustic waves in a plasma system. New families of exact closed-form solutions are obtained in hyperbolic, trigonometric, and rational function solutions with the available free constants. With the help of computerized symbolic computation work, the newly formed closed-form solutions are validated by back substituting them into the equations using the computational mathematical software. Furthermore, the graphical representations of all these obtained solutions are discussed and demonstrated by giving the suitable best values of arbitrary functions and constants via three-dimensional surface and density plots. The dynamics of the solution profiles demonstrate the annihilation of 3D kink-type soliton waves, shock waves, double solitons, and multi-soliton wave structures. |
| first_indexed | 2024-04-12T15:28:13Z |
| format | Article |
| id | doaj.art-95bc6724df364b4a97d8ae1a0cd98bb4 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-12T15:28:13Z |
| publishDate | 2022-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-95bc6724df364b4a97d8ae1a0cd98bb42022-12-22T03:27:12ZengElsevierResults in Physics2211-37972022-06-0137105504An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficientsSanjaya K. Mohanty0Sachin Kumar1Apul N. Dev2Manoj Kr. Deka3Dmitry V. Churikov4Oleg V. Kravchenko5Department of Mathematics, Siksha ‘O’ Anusandhan (Deemed to be University), Bhubaneswar 751030, Odisha, IndiaDepartment of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, IndiaCentre for Data Science, Siksha ‘O’ Anusandhan (Deemed to be University), Bhubaneswar 751030, Odisha, IndiaDepartment of Applied Science, Guwahati University 781014, Assam, IndiaScientific and Technological Centre of Unique Instrumentation of the Russian Academy of Sciences, Moscow, Russian FederationBauman Moscow State Technical University, Moscow, Russian Federation; Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russian Federation; Corresponding author at: Scientific and Technological Centre of Unique Instrumentation of the Russian Academy of Sciences, Moscow, Russian Federation.The extended generalized G′G–expansion is well defined and an efficient technique, which is used to obtain the exact traveling wave solutions to the governing nonlinear equations with constant coefficients as well as variable coefficients. In this paper, the modified Korteweg–de Vries (mKdV) equation and Burgers equation with variable coefficients are investigated through the extended generalized G′G–expansion method, which are exceptional cases of the nonlinear evolution equations widely used in a two-layer fluid system, in fluid-filled elastic tubes, in an atmospheric and oceanic dynamical system, traffic flow, turbulence in fluid dynamics, dusty plasma, ion-acoustic waves in a plasma system. New families of exact closed-form solutions are obtained in hyperbolic, trigonometric, and rational function solutions with the available free constants. With the help of computerized symbolic computation work, the newly formed closed-form solutions are validated by back substituting them into the equations using the computational mathematical software. Furthermore, the graphical representations of all these obtained solutions are discussed and demonstrated by giving the suitable best values of arbitrary functions and constants via three-dimensional surface and density plots. The dynamics of the solution profiles demonstrate the annihilation of 3D kink-type soliton waves, shock waves, double solitons, and multi-soliton wave structures.http://www.sciencedirect.com/science/article/pii/S2211379722002443Exact solutionsExtended generalized (G’/G)–expansion methodNonlinear partial differential equations with variable coefficientsSolitary waves |
| spellingShingle | Sanjaya K. Mohanty Sachin Kumar Apul N. Dev Manoj Kr. Deka Dmitry V. Churikov Oleg V. Kravchenko An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients Results in Physics Exact solutions Extended generalized (G’/G)–expansion method Nonlinear partial differential equations with variable coefficients Solitary waves |
| title | An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients |
| title_full | An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients |
| title_fullStr | An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients |
| title_full_unstemmed | An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients |
| title_short | An efficient technique of G′G–expansion method for modified KdV and Burgers equations with variable coefficients |
| title_sort | efficient technique of g g expansion method for modified kdv and burgers equations with variable coefficients |
| topic | Exact solutions Extended generalized (G’/G)–expansion method Nonlinear partial differential equations with variable coefficients Solitary waves |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722002443 |
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