Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions
Abstract We found, through analytical and numerical methods, new towers of infinite number of asymptotically conserved charges for deformations of the Korteweg-de Vries equation (KdV). It is shown analytically that the standard KdV also exhibits some towers of infinite number of anomalous charges, a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2020)136 |
| _version_ | 1818291518197202944 |
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| author | H. Blas R. Ochoa D. Suarez |
| author_facet | H. Blas R. Ochoa D. Suarez |
| author_sort | H. Blas |
| collection | DOAJ |
| description | Abstract We found, through analytical and numerical methods, new towers of infinite number of asymptotically conserved charges for deformations of the Korteweg-de Vries equation (KdV). It is shown analytically that the standard KdV also exhibits some towers of infinite number of anomalous charges, and that their relevant anomalies vanish for N −soliton solution. Some deformations of the KdV model are performed through the Riccati-type pseudo-potential approach, and infinite number of exact non-local conservation laws is provided using a linear formulation of the deformed model. In order to check the degrees of modifications of the charges around the soliton interaction regions, we compute numerically some representative anomalies, associated to the lowest order quasi-conservation laws, depending on the deformation parameters {ϵ 1, ϵ 2}, which include the standard KdV (ϵ 1 = ϵ 2 = 0), the regularized long-wave (RLW) (ϵ 1 = 1, ϵ 2 = 0), the modified regularized long-wave (mRLW) (ϵ 1 = ϵ 2 = 1) and the KdV-RLW (KdV-BBM) type (ϵ 2 = 0, ≠ = {0, 1}) equations, respectively. Our numerical simulations show the elastic scattering of two and three solitons for a wide range of values of the set {ϵ 1, ϵ 2}, for a variety of amplitudes and relative velocities. The KdV-type equations are quite ubiquitous in several areas of non-linear science, and they find relevant applications in the study of General Relativity on AdS 3, Bose-Einstein condensates, superconductivity and soliton gas and turbulence in fluid dynamics. |
| first_indexed | 2024-12-13T02:45:20Z |
| format | Article |
| id | doaj.art-4d558ce6726a4a5fab1491f0f0d82211 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T02:45:20Z |
| publishDate | 2020-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4d558ce6726a4a5fab1491f0f0d822112022-12-22T00:02:11ZengSpringerOpenJournal of High Energy Physics1029-84792020-03-012020315010.1007/JHEP03(2020)136Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisionsH. Blas0R. Ochoa1D. Suarez2Instituto de Física, Universidade Federal de Mato GrossoFacultad de Ciencias, Universidad Nacional de IngenieríaFacultad de Ciencias, Universidad Nacional de IngenieríaAbstract We found, through analytical and numerical methods, new towers of infinite number of asymptotically conserved charges for deformations of the Korteweg-de Vries equation (KdV). It is shown analytically that the standard KdV also exhibits some towers of infinite number of anomalous charges, and that their relevant anomalies vanish for N −soliton solution. Some deformations of the KdV model are performed through the Riccati-type pseudo-potential approach, and infinite number of exact non-local conservation laws is provided using a linear formulation of the deformed model. In order to check the degrees of modifications of the charges around the soliton interaction regions, we compute numerically some representative anomalies, associated to the lowest order quasi-conservation laws, depending on the deformation parameters {ϵ 1, ϵ 2}, which include the standard KdV (ϵ 1 = ϵ 2 = 0), the regularized long-wave (RLW) (ϵ 1 = 1, ϵ 2 = 0), the modified regularized long-wave (mRLW) (ϵ 1 = ϵ 2 = 1) and the KdV-RLW (KdV-BBM) type (ϵ 2 = 0, ≠ = {0, 1}) equations, respectively. Our numerical simulations show the elastic scattering of two and three solitons for a wide range of values of the set {ϵ 1, ϵ 2}, for a variety of amplitudes and relative velocities. The KdV-type equations are quite ubiquitous in several areas of non-linear science, and they find relevant applications in the study of General Relativity on AdS 3, Bose-Einstein condensates, superconductivity and soliton gas and turbulence in fluid dynamics.http://link.springer.com/article/10.1007/JHEP03(2020)136Integrable Field TheoriesSolitons Monopoles and InstantonsField Theories in Lower DimensionsIntegrable Hierarchies |
| spellingShingle | H. Blas R. Ochoa D. Suarez Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions Journal of High Energy Physics Integrable Field Theories Solitons Monopoles and Instantons Field Theories in Lower Dimensions Integrable Hierarchies |
| title | Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions |
| title_full | Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions |
| title_fullStr | Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions |
| title_full_unstemmed | Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions |
| title_short | Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions |
| title_sort | quasi integrable kdv models towers of infinite number of anomalous charges and soliton collisions |
| topic | Integrable Field Theories Solitons Monopoles and Instantons Field Theories in Lower Dimensions Integrable Hierarchies |
| url | http://link.springer.com/article/10.1007/JHEP03(2020)136 |
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