New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations
A large family of explicit exact solutions to both Korteweg- de Vries and modified Korteweg- de Vries equations are determined by the implementation of the new extended direct algebraic method. The procedure starts by reducing both equations to related ODEs by compatible travelling wave transforms....
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2020-10-01
|
| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amns.2020.2.00034 |
| _version_ | 1818745169154932736 |
|---|---|
| author | Rezazadeh Hadi Korkmaz Alper EL Achab Abdelfattah Adel Waleed Bekir Ahmet |
| author_facet | Rezazadeh Hadi Korkmaz Alper EL Achab Abdelfattah Adel Waleed Bekir Ahmet |
| author_sort | Rezazadeh Hadi |
| collection | DOAJ |
| description | A large family of explicit exact solutions to both Korteweg- de Vries and modified Korteweg- de Vries equations are determined by the implementation of the new extended direct algebraic method. The procedure starts by reducing both equations to related ODEs by compatible travelling wave transforms. The balance between the highest degree nonlinear and highest order derivative terms gives the degree of the finite series. Substitution of the assumed solution and some algebra results in a system of equations are found. The relation between the parameters is determined by solving this system. The solutions of travelling wave forms determined by the application of the approach are represented in explicit functions of some generalized trigonometric and hyperbolic functions and exponential function. Some more solutions with different characteristics are also found. |
| first_indexed | 2024-12-18T02:55:55Z |
| format | Article |
| id | doaj.art-f12b765b544f4ee2b01cda91208d1567 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-12-18T02:55:55Z |
| publishDate | 2020-10-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-f12b765b544f4ee2b01cda91208d15672022-12-21T21:23:22ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562020-10-016144745810.2478/amns.2020.2.00034New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV EquationsRezazadeh Hadi0Korkmaz Alper1EL Achab Abdelfattah2Adel Waleed3Bekir Ahmet4Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, IranNord Staße 9Weimar, GermanyFaculty of Sciences Semlalia, Department of Mathematics, Cadi Ayyad University, B.d. du Prince Moulay Abdellah B.P.2390Marrakech, MoroccoFaculty of Engineering, Department of Mathematics and Engineering Physics, Mansoura University, EgyptNeighbourhood of Akcaglan, Imarli Street, Eskisehir26030, TurkeyA large family of explicit exact solutions to both Korteweg- de Vries and modified Korteweg- de Vries equations are determined by the implementation of the new extended direct algebraic method. The procedure starts by reducing both equations to related ODEs by compatible travelling wave transforms. The balance between the highest degree nonlinear and highest order derivative terms gives the degree of the finite series. Substitution of the assumed solution and some algebra results in a system of equations are found. The relation between the parameters is determined by solving this system. The solutions of travelling wave forms determined by the application of the approach are represented in explicit functions of some generalized trigonometric and hyperbolic functions and exponential function. Some more solutions with different characteristics are also found.https://doi.org/10.2478/amns.2020.2.00034new extended direct algebraic methodkdv equationmodified kdv equationexact solutiontravelling wave solution35c0735c0883c15 |
| spellingShingle | Rezazadeh Hadi Korkmaz Alper EL Achab Abdelfattah Adel Waleed Bekir Ahmet New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations Applied Mathematics and Nonlinear Sciences new extended direct algebraic method kdv equation modified kdv equation exact solution travelling wave solution 35c07 35c08 83c15 |
| title | New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations |
| title_full | New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations |
| title_fullStr | New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations |
| title_full_unstemmed | New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations |
| title_short | New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations |
| title_sort | new travelling wave solution based new riccati equation for solving kdv and modified kdv equations |
| topic | new extended direct algebraic method kdv equation modified kdv equation exact solution travelling wave solution 35c07 35c08 83c15 |
| url | https://doi.org/10.2478/amns.2020.2.00034 |
| work_keys_str_mv | AT rezazadehhadi newtravellingwavesolutionbasednewriccatiequationforsolvingkdvandmodifiedkdvequations AT korkmazalper newtravellingwavesolutionbasednewriccatiequationforsolvingkdvandmodifiedkdvequations AT elachababdelfattah newtravellingwavesolutionbasednewriccatiequationforsolvingkdvandmodifiedkdvequations AT adelwaleed newtravellingwavesolutionbasednewriccatiequationforsolvingkdvandmodifiedkdvequations AT bekirahmet newtravellingwavesolutionbasednewriccatiequationforsolvingkdvandmodifiedkdvequations |