Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations
A technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It is solved through this refine...
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MDPI AG
2021-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/8/1529 |
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| author | Rodica Cimpoiasu Radu Constantinescu Alina Streche Pauna |
| author_facet | Rodica Cimpoiasu Radu Constantinescu Alina Streche Pauna |
| author_sort | Rodica Cimpoiasu |
| collection | DOAJ |
| description | A technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It is solved through this refined version of the auxiliary equation technique, and multiparametric solutions are found. The key idea is that the general elliptic equation, considered here as an auxiliary equation, degenerates under some special conditions into subequations involving fewer parameters. Using these subequations, we successfully construct, in a unitary way, a series of solutions for the BD equation, part of them not yet reported. The technique of multiple auxiliary equations could be employed to handle several other types of nonlinear equations, from QFT and from various other scientific areas. |
| first_indexed | 2024-03-10T08:19:50Z |
| format | Article |
| id | doaj.art-b86fe3795400482c8caa15ec0c247a06 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T08:19:50Z |
| publishDate | 2021-08-01 |
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| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b86fe3795400482c8caa15ec0c247a062023-11-22T10:03:00ZengMDPI AGSymmetry2073-89942021-08-01138152910.3390/sym13081529Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type EquationsRodica Cimpoiasu0Radu Constantinescu1Alina Streche Pauna2Department of Physics, University of Craiova, 13 A.I. Cuza Street, 200585 Craiova, RomaniaDepartment of Physics, University of Craiova, 13 A.I. Cuza Street, 200585 Craiova, RomaniaDepartment of Physics, University of Craiova, 13 A.I. Cuza Street, 200585 Craiova, RomaniaA technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It is solved through this refined version of the auxiliary equation technique, and multiparametric solutions are found. The key idea is that the general elliptic equation, considered here as an auxiliary equation, degenerates under some special conditions into subequations involving fewer parameters. Using these subequations, we successfully construct, in a unitary way, a series of solutions for the BD equation, part of them not yet reported. The technique of multiple auxiliary equations could be employed to handle several other types of nonlinear equations, from QFT and from various other scientific areas.https://www.mdpi.com/2073-8994/13/8/1529scalar field theoryBullough–Dodd equationmultiple auxiliary equationstraveling wave solutions |
| spellingShingle | Rodica Cimpoiasu Radu Constantinescu Alina Streche Pauna Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations Symmetry scalar field theory Bullough–Dodd equation multiple auxiliary equations traveling wave solutions |
| title | Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations |
| title_full | Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations |
| title_fullStr | Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations |
| title_full_unstemmed | Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations |
| title_short | Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations |
| title_sort | solutions of the bullough dodd model of scalar field through jacobi type equations |
| topic | scalar field theory Bullough–Dodd equation multiple auxiliary equations traveling wave solutions |
| url | https://www.mdpi.com/2073-8994/13/8/1529 |
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