Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity
This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fas...
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| Format: | Article |
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College of Science for Women/ University of Baghdad
2021
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| Online Access: | https://eprints.ums.edu.my/id/eprint/27220/1/Approximate%20analytical%20solutions%20of%20bright%20optical%20soliton%20for%20Nonlinear%20Schr%C3%B6dinger%20Equation%20of%20power%20law%20nonlinearity%20FULLTEXT.pdf https://eprints.ums.edu.my/id/eprint/27220/2/Approximate%20analytical%20solutions%20of%20bright%20optical%20soliton%20for%20Nonlinear%20Schr%C3%B6dinger%20Equation%20of%20power%20law%20nonlinearity%20ABSTRACT.pdf |
| _version_ | 1825714124013699072 |
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| author | Che Haziqah Che Hussin Amirah Azmi Ahmad Izani Md Ismail Adem Kilicman Ishak Hashim |
| author_facet | Che Haziqah Che Hussin Amirah Azmi Ahmad Izani Md Ismail Adem Kilicman Ishak Hashim |
| author_sort | Che Haziqah Che Hussin |
| collection | UMS |
| description | This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a wide time frame. Two examples are provided for showing the ability and advantages of the proposed method to approximate the solution of the power law nonlinearity of NLSEs. For pictorial representation, graphical inputs are included to represent the solution and show the precision as well as the validity of the MMRDTM. |
| first_indexed | 2024-03-06T03:07:08Z |
| format | Article |
| id | ums.eprints-27220 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:07:08Z |
| publishDate | 2021 |
| publisher | College of Science for Women/ University of Baghdad |
| record_format | dspace |
| spelling | ums.eprints-272202021-06-14T06:59:43Z https://eprints.ums.edu.my/id/eprint/27220/ Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity Che Haziqah Che Hussin Amirah Azmi Ahmad Izani Md Ismail Adem Kilicman Ishak Hashim QA Mathematics This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a wide time frame. Two examples are provided for showing the ability and advantages of the proposed method to approximate the solution of the power law nonlinearity of NLSEs. For pictorial representation, graphical inputs are included to represent the solution and show the precision as well as the validity of the MMRDTM. College of Science for Women/ University of Baghdad 2021 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/27220/1/Approximate%20analytical%20solutions%20of%20bright%20optical%20soliton%20for%20Nonlinear%20Schr%C3%B6dinger%20Equation%20of%20power%20law%20nonlinearity%20FULLTEXT.pdf text en https://eprints.ums.edu.my/id/eprint/27220/2/Approximate%20analytical%20solutions%20of%20bright%20optical%20soliton%20for%20Nonlinear%20Schr%C3%B6dinger%20Equation%20of%20power%20law%20nonlinearity%20ABSTRACT.pdf Che Haziqah Che Hussin and Amirah Azmi and Ahmad Izani Md Ismail and Adem Kilicman and Ishak Hashim (2021) Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity. Baghdad Science Journal, 18 (1). pp. 836-845. ISSN 2411-7986 https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5920/3423 https://doi.org/10.21123/bsj.2021.18.1(Suppl.).0836 https://doi.org/10.21123/bsj.2021.18.1(Suppl.).0836 |
| spellingShingle | QA Mathematics Che Haziqah Che Hussin Amirah Azmi Ahmad Izani Md Ismail Adem Kilicman Ishak Hashim Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity |
| title | Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity |
| title_full | Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity |
| title_fullStr | Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity |
| title_full_unstemmed | Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity |
| title_short | Approximate analytical solutions of bright optical soliton for Nonlinear Schrödinger Equation of power law nonlinearity |
| title_sort | approximate analytical solutions of bright optical soliton for nonlinear schrodinger equation of power law nonlinearity |
| topic | QA Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/27220/1/Approximate%20analytical%20solutions%20of%20bright%20optical%20soliton%20for%20Nonlinear%20Schr%C3%B6dinger%20Equation%20of%20power%20law%20nonlinearity%20FULLTEXT.pdf https://eprints.ums.edu.my/id/eprint/27220/2/Approximate%20analytical%20solutions%20of%20bright%20optical%20soliton%20for%20Nonlinear%20Schr%C3%B6dinger%20Equation%20of%20power%20law%20nonlinearity%20ABSTRACT.pdf |
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