Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System
Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/9457078 |
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| author | Sheng Zhang Siyu Hong |
| author_facet | Sheng Zhang Siyu Hong |
| author_sort | Sheng Zhang |
| collection | DOAJ |
| description | Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform (IST) method. Finally, in the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. When n=1 and n=2, the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures. |
| format | Article |
| id | doaj-art-0cb745768b874a4bb164d0bfc5272f9e |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-0cb745768b874a4bb164d0bfc5272f9e2025-02-03T01:12:00ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/94570789457078Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential SystemSheng Zhang0Siyu Hong1School of Mathematics and Physics, Bohai University, Jinzhou 121013, ChinaSchool of Mathematics and Physics, Bohai University, Jinzhou 121013, ChinaSearching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform (IST) method. Finally, in the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. When n=1 and n=2, the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures.http://dx.doi.org/10.1155/2017/9457078 |
| spellingShingle | Sheng Zhang Siyu Hong Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System Complexity |
| title | Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System |
| title_full | Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System |
| title_fullStr | Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System |
| title_full_unstemmed | Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System |
| title_short | Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System |
| title_sort | lax integrability and soliton solutions for a nonisospectral integrodifferential system |
| url | http://dx.doi.org/10.1155/2017/9457078 |
| work_keys_str_mv | AT shengzhang laxintegrabilityandsolitonsolutionsforanonisospectralintegrodifferentialsystem AT siyuhong laxintegrabilityandsolitonsolutionsforanonisospectralintegrodifferentialsystem |