Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering
In this work, we study the generalized 2D equal-width equation which arises in various fields of science. With the aid of numerous methods which includes Lie symmetry analysis, power series expansion and Weierstrass method, we produce closed-form solutions of this model. The exact solutions obtained...
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| Format: | Article |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/1/24 |
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| author | Chaudry Masood Khalique Karabo Plaatjie |
| author_facet | Chaudry Masood Khalique Karabo Plaatjie |
| author_sort | Chaudry Masood Khalique |
| collection | DOAJ |
| description | In this work, we study the generalized 2D equal-width equation which arises in various fields of science. With the aid of numerous methods which includes Lie symmetry analysis, power series expansion and Weierstrass method, we produce closed-form solutions of this model. The exact solutions obtained are the snoidal wave, cnoidal wave, Weierstrass elliptic function, Jacobi elliptic cosine function, solitary wave and exponential function solutions. Moreover, we give a graphical representation of the obtained solutions using certain parametric values. Furthermore, the conserved vectors of the underlying equation are constructed by utilizing two approaches: the multiplier method and Noether’s theorem. The multiplier method provided us with four local conservation laws, whereas Noether’s theorem yielded five nonlocal conservation laws. The conservation laws that are constructed contain the conservation of energy and momentum. |
| first_indexed | 2024-03-10T03:33:09Z |
| format | Article |
| id | doaj.art-c0b9f91371844b3ab53ab21a829e63ea |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:33:09Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-c0b9f91371844b3ab53ab21a829e63ea2023-11-23T11:52:58ZengMDPI AGMathematics2227-73902021-12-011012410.3390/math10010024Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of EngineeringChaudry Masood Khalique0Karabo Plaatjie1Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, Mafikeng Campus, North-West University, Private Bag X 2046, Mmabatho 2735, South AfricaDepartment of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, Mafikeng Campus, North-West University, Private Bag X 2046, Mmabatho 2735, South AfricaIn this work, we study the generalized 2D equal-width equation which arises in various fields of science. With the aid of numerous methods which includes Lie symmetry analysis, power series expansion and Weierstrass method, we produce closed-form solutions of this model. The exact solutions obtained are the snoidal wave, cnoidal wave, Weierstrass elliptic function, Jacobi elliptic cosine function, solitary wave and exponential function solutions. Moreover, we give a graphical representation of the obtained solutions using certain parametric values. Furthermore, the conserved vectors of the underlying equation are constructed by utilizing two approaches: the multiplier method and Noether’s theorem. The multiplier method provided us with four local conservation laws, whereas Noether’s theorem yielded five nonlocal conservation laws. The conservation laws that are constructed contain the conservation of energy and momentum.https://www.mdpi.com/2227-7390/10/1/24generalized 2D equal-width equationexact solutionWeierstrass elliptic functionsKudryashov’s methodconservation lawsNoether’s theorem |
| spellingShingle | Chaudry Masood Khalique Karabo Plaatjie Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering Mathematics generalized 2D equal-width equation exact solution Weierstrass elliptic functions Kudryashov’s method conservation laws Noether’s theorem |
| title | Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering |
| title_full | Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering |
| title_fullStr | Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering |
| title_full_unstemmed | Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering |
| title_short | Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering |
| title_sort | symmetry methods and conservation laws for the nonlinear generalized 2d equal width partial differential equation of engineering |
| topic | generalized 2D equal-width equation exact solution Weierstrass elliptic functions Kudryashov’s method conservation laws Noether’s theorem |
| url | https://www.mdpi.com/2227-7390/10/1/24 |
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