Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves
In this article, we successfully obtain novel solutions for the coupled Drinfel’d–Sokolov–Wilson DSW system utilizing various methods. These include soliton solutions characterized by hyperbolic, rational, and trigonometric functions. Specifically, the generalized exponential rational function metho...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-11-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/22/4598 |
| _version_ | 1797458542603534336 |
|---|---|
| author | Sumayah Hamzah Alhejaili Abdulghani Alharbi |
| author_facet | Sumayah Hamzah Alhejaili Abdulghani Alharbi |
| author_sort | Sumayah Hamzah Alhejaili |
| collection | DOAJ |
| description | In this article, we successfully obtain novel solutions for the coupled Drinfel’d–Sokolov–Wilson DSW system utilizing various methods. These include soliton solutions characterized by hyperbolic, rational, and trigonometric functions. Specifically, the generalized exponential rational function method (GERFM) and a modified version of the new Kudryashov method (MVNK) are employed to derive diverse soliton solutions for the system. Additionally, we demonstrate numerical solutions for the coupled Drinfel’d–Sokolov–Wilson system using adaptive moving mesh and uniform mesh methods. Also, we study the stability and error analysis of the numerical schemes. To validate the accuracy and reliability of the exact solutions obtained through analytical methods, we compare them with the numerical solutions both analytically and graphically. The techniques presented in this article are deemed suitable and acceptable and can be effectively applied to solve other nonlinear evolution systems. |
| first_indexed | 2024-03-09T16:38:38Z |
| format | Article |
| id | doaj.art-d8d31d69589c4ad9b88693e969854372 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:38:38Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d8d31d69589c4ad9b88693e9698543722023-11-24T14:54:08ZengMDPI AGMathematics2227-73902023-11-011122459810.3390/math11224598Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water WavesSumayah Hamzah Alhejaili0Abdulghani Alharbi1Department of Mathematics, College of Science, Taibah University, Al-Madinah al-Munawwarah 42353, Saudi ArabiaDepartment of Mathematics, College of Science, Taibah University, Al-Madinah al-Munawwarah 42353, Saudi ArabiaIn this article, we successfully obtain novel solutions for the coupled Drinfel’d–Sokolov–Wilson DSW system utilizing various methods. These include soliton solutions characterized by hyperbolic, rational, and trigonometric functions. Specifically, the generalized exponential rational function method (GERFM) and a modified version of the new Kudryashov method (MVNK) are employed to derive diverse soliton solutions for the system. Additionally, we demonstrate numerical solutions for the coupled Drinfel’d–Sokolov–Wilson system using adaptive moving mesh and uniform mesh methods. Also, we study the stability and error analysis of the numerical schemes. To validate the accuracy and reliability of the exact solutions obtained through analytical methods, we compare them with the numerical solutions both analytically and graphically. The techniques presented in this article are deemed suitable and acceptable and can be effectively applied to solve other nonlinear evolution systems.https://www.mdpi.com/2227-7390/11/22/4598coupled Drinfel’d–Sokolov–Wilson systemexact solutionnumerical solutionwavesadaptive moving mesh methoduniform mesh |
| spellingShingle | Sumayah Hamzah Alhejaili Abdulghani Alharbi Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves Mathematics coupled Drinfel’d–Sokolov–Wilson system exact solution numerical solution waves adaptive moving mesh method uniform mesh |
| title | Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves |
| title_full | Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves |
| title_fullStr | Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves |
| title_full_unstemmed | Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves |
| title_short | Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves |
| title_sort | structure of analytical and numerical wave solutions for the nonlinear 1 1 coupled drinfel d sokolov wilson system arising in shallow water waves |
| topic | coupled Drinfel’d–Sokolov–Wilson system exact solution numerical solution waves adaptive moving mesh method uniform mesh |
| url | https://www.mdpi.com/2227-7390/11/22/4598 |
| work_keys_str_mv | AT sumayahhamzahalhejaili structureofanalyticalandnumericalwavesolutionsforthenonlinear11coupleddrinfeldsokolovwilsonsystemarisinginshallowwaterwaves AT abdulghanialharbi structureofanalyticalandnumericalwavesolutionsforthenonlinear11coupleddrinfeldsokolovwilsonsystemarisinginshallowwaterwaves |