Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation
In this work, we investigate a (3+1)-dimensional generalised Kadomtsev–Petviashvili equation, recently introduced in the literature. We determine its group invariant solutions by employing Lie symmetry methods and obtain elliptic, rational and logarithmic solutions. The solutions derived in this pap...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/6/1012 |
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| author | Innocent Simbanefayi Chaudry Masood Khalique |
| author_facet | Innocent Simbanefayi Chaudry Masood Khalique |
| author_sort | Innocent Simbanefayi |
| collection | DOAJ |
| description | In this work, we investigate a (3+1)-dimensional generalised Kadomtsev–Petviashvili equation, recently introduced in the literature. We determine its group invariant solutions by employing Lie symmetry methods and obtain elliptic, rational and logarithmic solutions. The solutions derived in this paper are the most general since they contain elliptic functions. Finally, we derive the conserved quantities of this equation by employing two approaches—the general multiplier approach and Ibragimov’s theorem. The importance of conservation laws is explained in the introduction. It should be pointed out that the investigation of higher dimensional nonlinear partial differential equations is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena. |
| first_indexed | 2024-03-10T19:01:26Z |
| format | Article |
| id | doaj.art-9d4fe13c614145109d6aca61bdd8edc0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T19:01:26Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9d4fe13c614145109d6aca61bdd8edc02023-11-20T04:26:56ZengMDPI AGMathematics2227-73902020-06-0186101210.3390/math8061012Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili EquationInnocent Simbanefayi0Chaudry Masood Khalique1International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaInternational Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaIn this work, we investigate a (3+1)-dimensional generalised Kadomtsev–Petviashvili equation, recently introduced in the literature. We determine its group invariant solutions by employing Lie symmetry methods and obtain elliptic, rational and logarithmic solutions. The solutions derived in this paper are the most general since they contain elliptic functions. Finally, we derive the conserved quantities of this equation by employing two approaches—the general multiplier approach and Ibragimov’s theorem. The importance of conservation laws is explained in the introduction. It should be pointed out that the investigation of higher dimensional nonlinear partial differential equations is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena.https://www.mdpi.com/2227-7390/8/6/1012(3+1)-dimensional generalised KP equationinvariant solutionsmultiplier methodIbragimov’s conservation theoremconserved quantities |
| spellingShingle | Innocent Simbanefayi Chaudry Masood Khalique Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation Mathematics (3+1)-dimensional generalised KP equation invariant solutions multiplier method Ibragimov’s conservation theorem conserved quantities |
| title | Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation |
| title_full | Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation |
| title_fullStr | Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation |
| title_full_unstemmed | Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation |
| title_short | Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation |
| title_sort | group invariant solutions and conserved quantities of a 3 1 dimensional generalized kadomtsev petviashvili equation |
| topic | (3+1)-dimensional generalised KP equation invariant solutions multiplier method Ibragimov’s conservation theorem conserved quantities |
| url | https://www.mdpi.com/2227-7390/8/6/1012 |
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