Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method
Abstract The prevalence of the use of mathematical software has dramatically influenced the evolution of differential equations. The use of these useful tools leads to faster advances in the presentation of numerical and analytical methods. This paper retrieves several soliton solutions to the fract...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-07-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02787-7 |
| _version_ | 1828804933002985472 |
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| author | Behzad Ghanbari Kottakkaran Sooppy Nisar Mujahed Aldhaifallah |
| author_facet | Behzad Ghanbari Kottakkaran Sooppy Nisar Mujahed Aldhaifallah |
| author_sort | Behzad Ghanbari |
| collection | DOAJ |
| description | Abstract The prevalence of the use of mathematical software has dramatically influenced the evolution of differential equations. The use of these useful tools leads to faster advances in the presentation of numerical and analytical methods. This paper retrieves several soliton solutions to the fractional perturbed Schrödinger’s equation with Kerr and parabolic law nonlinearity, and local conformable derivative. The method used in this article, called the generalized exponential rational function method, also relies heavily on the use of symbolic software such as Maple. The considered model has prominent applications in water optical metamaterials. The method retrieves several exponential, hyperbolic, and trigonometric function solutions to the model. The numerical evolution of the obtained solutions is also exhibited. The resulted wide range of solutions derived from the method proves its effectiveness in solving the model under investigation. It is also recommended to use the technique used in this article to solve similar problems. |
| first_indexed | 2024-12-12T07:47:24Z |
| format | Article |
| id | doaj.art-1ac79e7bf5c04011ab2ac2432b9d68e6 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T07:47:24Z |
| publishDate | 2020-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-1ac79e7bf5c04011ab2ac2432b9d68e62022-12-22T00:32:32ZengSpringerOpenAdvances in Difference Equations1687-18472020-07-012020112510.1186/s13662-020-02787-7Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration methodBehzad Ghanbari0Kottakkaran Sooppy Nisar1Mujahed Aldhaifallah2Department of Engineering Science, Kermanshah University of TechnologyDepartment of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz UniversitySystems Engineering Department, King Fahd University of Petroleum and MineralsAbstract The prevalence of the use of mathematical software has dramatically influenced the evolution of differential equations. The use of these useful tools leads to faster advances in the presentation of numerical and analytical methods. This paper retrieves several soliton solutions to the fractional perturbed Schrödinger’s equation with Kerr and parabolic law nonlinearity, and local conformable derivative. The method used in this article, called the generalized exponential rational function method, also relies heavily on the use of symbolic software such as Maple. The considered model has prominent applications in water optical metamaterials. The method retrieves several exponential, hyperbolic, and trigonometric function solutions to the model. The numerical evolution of the obtained solutions is also exhibited. The resulted wide range of solutions derived from the method proves its effectiveness in solving the model under investigation. It is also recommended to use the technique used in this article to solve similar problems.http://link.springer.com/article/10.1186/s13662-020-02787-7GERFMWave solutions to PDEsFractional operatorsPerturbed nonlinear Schrödinger’s equationSymbolic manipulationNonlinearity laws |
| spellingShingle | Behzad Ghanbari Kottakkaran Sooppy Nisar Mujahed Aldhaifallah Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method Advances in Difference Equations GERFM Wave solutions to PDEs Fractional operators Perturbed nonlinear Schrödinger’s equation Symbolic manipulation Nonlinearity laws |
| title | Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method |
| title_full | Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method |
| title_fullStr | Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method |
| title_full_unstemmed | Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method |
| title_short | Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method |
| title_sort | abundant solitary wave solutions to an extended nonlinear schrodinger s equation with conformable derivative using an efficient integration method |
| topic | GERFM Wave solutions to PDEs Fractional operators Perturbed nonlinear Schrödinger’s equation Symbolic manipulation Nonlinearity laws |
| url | http://link.springer.com/article/10.1186/s13662-020-02787-7 |
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