A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation
In this current study, the potential-KdV equation has been altered by the addition of a new stochastic term. The transmission of nonlinear optical solitons and photons is described by the new stochastic potential-KdV (spKdV), which applies to electric circuits and multi-component plasmas. The Lie sy...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-01-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723010951 |
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| author | Naseem Abbas Akhtar Hussain Muhammad Bilal Riaz Tarek F. Ibrahim F.M. Osman Birkea R. Abdelrahman Tahir |
| author_facet | Naseem Abbas Akhtar Hussain Muhammad Bilal Riaz Tarek F. Ibrahim F.M. Osman Birkea R. Abdelrahman Tahir |
| author_sort | Naseem Abbas |
| collection | DOAJ |
| description | In this current study, the potential-KdV equation has been altered by the addition of a new stochastic term. The transmission of nonlinear optical solitons and photons is described by the new stochastic potential-KdV (spKdV), which applies to electric circuits and multi-component plasmas. The Lie symmetry approach is presented to find out the symmetry generators. The matrices method is applied to develop the one-dimensional optimal system for the acquired Lie algebra. Based on each element of the one-dimensional optimal system, symmetry reductions are used to reduce the considered model into nonlinear ordinary differential equations (ODEs). One of these nonlinear ODEs is solved using a new novel generalized exponential rational function (GERF) approach. Graphical interpretation of a few of the acquired results is added by taking the suitable values of the constants. A novel general theorem which is known as Ibragimov’s theorem enables the computation of conservation laws for any differential equation, without requiring the presence of Lagrangians. The idea of the self-adjoint equations for nonlinear equations serves as the foundation for this theorem. We present that the spKdV equation is nonlinearly self-adjoint. The conserved quantities are computed in line with each symmetry generator using Ibragimov’s theorem. |
| first_indexed | 2024-03-08T12:52:24Z |
| format | Article |
| id | doaj.art-7391dd1111db49dc8822709313a46443 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-08T12:52:24Z |
| publishDate | 2024-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-7391dd1111db49dc8822709313a464432024-01-20T04:45:22ZengElsevierResults in Physics2211-37972024-01-0156107302A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equationNaseem Abbas0Akhtar Hussain1Muhammad Bilal Riaz2Tarek F. Ibrahim3F.M. Osman Birkea4R. Abdelrahman Tahir5Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan; Corresponding author.IT4Innovations, VSB - Technical University of Ostrava, Ostrava, Czech Republic; Department of Computer Science and Mathematics, Lebanese American University, Byblos, LebanonDepartment of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University, Abha, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Northern Border University, Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi ArabiaIn this current study, the potential-KdV equation has been altered by the addition of a new stochastic term. The transmission of nonlinear optical solitons and photons is described by the new stochastic potential-KdV (spKdV), which applies to electric circuits and multi-component plasmas. The Lie symmetry approach is presented to find out the symmetry generators. The matrices method is applied to develop the one-dimensional optimal system for the acquired Lie algebra. Based on each element of the one-dimensional optimal system, symmetry reductions are used to reduce the considered model into nonlinear ordinary differential equations (ODEs). One of these nonlinear ODEs is solved using a new novel generalized exponential rational function (GERF) approach. Graphical interpretation of a few of the acquired results is added by taking the suitable values of the constants. A novel general theorem which is known as Ibragimov’s theorem enables the computation of conservation laws for any differential equation, without requiring the presence of Lagrangians. The idea of the self-adjoint equations for nonlinear equations serves as the foundation for this theorem. We present that the spKdV equation is nonlinearly self-adjoint. The conserved quantities are computed in line with each symmetry generator using Ibragimov’s theorem.http://www.sciencedirect.com/science/article/pii/S2211379723010951Stochastic potential-KdV equationSymmetriesOptimal systemSimilarity reductionsNonlinear self adjointConservation laws |
| spellingShingle | Naseem Abbas Akhtar Hussain Muhammad Bilal Riaz Tarek F. Ibrahim F.M. Osman Birkea R. Abdelrahman Tahir A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation Results in Physics Stochastic potential-KdV equation Symmetries Optimal system Similarity reductions Nonlinear self adjoint Conservation laws |
| title | A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation |
| title_full | A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation |
| title_fullStr | A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation |
| title_full_unstemmed | A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation |
| title_short | A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation |
| title_sort | discussion on the lie symmetry analysis travelling wave solutions and conservation laws of new generalized stochastic potential kdv equation |
| topic | Stochastic potential-KdV equation Symmetries Optimal system Similarity reductions Nonlinear self adjoint Conservation laws |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723010951 |
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