Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients
The nonlinear Schrödinger (NLS) types of equations play a key role in quantum mechanics, Quantum communication and physical applications. However, how to deal with explicit solutions and other properties of the NLS equations, especially for the variable-coefficient NLS (vc-NLS) types of equations is...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321323002328 |
| _version_ | 1797736867433545728 |
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| author | Hanze Liu |
| author_facet | Hanze Liu |
| author_sort | Hanze Liu |
| collection | DOAJ |
| description | The nonlinear Schrödinger (NLS) types of equations play a key role in quantum mechanics, Quantum communication and physical applications. However, how to deal with explicit solutions and other properties of the NLS equations, especially for the variable-coefficient NLS (vc-NLS) types of equations is a difficult problem. In this paper, we construct the form-preserving equivalent transformations (ETs) to transform the vc-NLS systems into constant-coefficient NLS (cc-NLS) systems, and the form-preserving ETs are given explicitly. Then, based on the equivalent transformation method, we deal with the integrability of the NLS equations, and the Lax pairs (LPs) are provided as verification of the integrability. |
| first_indexed | 2024-03-12T13:20:15Z |
| format | Article |
| id | doaj.art-4086e0e82295412b88f6337ff22b502a |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-03-12T13:20:15Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-4086e0e82295412b88f6337ff22b502a2023-08-26T04:42:42ZengElsevierNuclear Physics B0550-32132023-09-01994116303Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficientsHanze Liu0School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252059, China; School of Mathematics and Statistics, Kashi University, Kashi 844006, China; Correspondence to: School of Mathematics and Statistics, Kashi University, No. 380 Xuefu Road, Dongcheng district, Kashi City, Xinjiang Uygur Autonomous Region 844006, China.The nonlinear Schrödinger (NLS) types of equations play a key role in quantum mechanics, Quantum communication and physical applications. However, how to deal with explicit solutions and other properties of the NLS equations, especially for the variable-coefficient NLS (vc-NLS) types of equations is a difficult problem. In this paper, we construct the form-preserving equivalent transformations (ETs) to transform the vc-NLS systems into constant-coefficient NLS (cc-NLS) systems, and the form-preserving ETs are given explicitly. Then, based on the equivalent transformation method, we deal with the integrability of the NLS equations, and the Lax pairs (LPs) are provided as verification of the integrability.http://www.sciencedirect.com/science/article/pii/S0550321323002328 |
| spellingShingle | Hanze Liu Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients Nuclear Physics B |
| title | Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients |
| title_full | Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients |
| title_fullStr | Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients |
| title_full_unstemmed | Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients |
| title_short | Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients |
| title_sort | equivalent transformation and integrability of the nonlinear schrodinger equations with time dependent coefficients |
| url | http://www.sciencedirect.com/science/article/pii/S0550321323002328 |
| work_keys_str_mv | AT hanzeliu equivalenttransformationandintegrabilityofthenonlinearschrodingerequationswithtimedependentcoefficients |