Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation
In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar struc...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/8851043 |
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| author | Irfan Mahmood Muhammad Waseem |
| author_facet | Irfan Mahmood Muhammad Waseem |
| author_sort | Irfan Mahmood |
| collection | DOAJ |
| description | In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation of the classical Painlevé second equation to the N-th form in terms of Wranskian. |
| format | Article |
| id | doaj-art-196ef712831f4afdb4c77e284420a4c6 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-196ef712831f4afdb4c77e284420a4c62025-02-03T01:00:15ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/88510438851043Lax Representation and Darboux Solutions of the Classical Painlevé Second EquationIrfan Mahmood0Muhammad Waseem1Centre for High Energy Physics, University of the Punjab, Lahore 54590, PakistanCentre for High Energy Physics, University of the Punjab, Lahore 54590, PakistanIn this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation of the classical Painlevé second equation to the N-th form in terms of Wranskian.http://dx.doi.org/10.1155/2021/8851043 |
| spellingShingle | Irfan Mahmood Muhammad Waseem Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation Advances in Mathematical Physics |
| title | Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation |
| title_full | Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation |
| title_fullStr | Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation |
| title_full_unstemmed | Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation |
| title_short | Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation |
| title_sort | lax representation and darboux solutions of the classical painleve second equation |
| url | http://dx.doi.org/10.1155/2021/8851043 |
| work_keys_str_mv | AT irfanmahmood laxrepresentationanddarbouxsolutionsoftheclassicalpainlevesecondequation AT muhammadwaseem laxrepresentationanddarbouxsolutionsoftheclassicalpainlevesecondequation |