Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension
We establish existence and uniqueness of solutions to the Cauchy problem associated with a new one-dimensional weakly-nonlinear, weakly-dispersive system which arises as an asymptotical approximation of the full potential theory equations for modelling propagation of small amplitude water waves on t...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/805625 |
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| _version_ | 1832557042788728832 |
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| author | Juan Carlos Muñoz Grajales |
| author_facet | Juan Carlos Muñoz Grajales |
| author_sort | Juan Carlos Muñoz Grajales |
| collection | DOAJ |
| description | We establish existence and uniqueness of solutions to the Cauchy problem associated with a new one-dimensional weakly-nonlinear, weakly-dispersive system which arises as an asymptotical approximation of the full potential theory equations for modelling propagation of small amplitude water waves on the surface of a shallow channel with variable depth, taking into account the effect of surface tension. Furthermore, numerical schemes of spectral type are introduced for approximating the evolution in time of solutions of this system and its travelling wave solutions, in both the periodic and nonperiodic case. |
| format | Article |
| id | doaj-art-9facbdad3a084b6095037225633e587c |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-9facbdad3a084b6095037225633e587c2025-02-03T05:43:52ZengWileyInternational Journal of Differential Equations1687-96431687-96512015-01-01201510.1155/2015/805625805625Propagation of Water Waves over Uneven Bottom under the Effect of Surface TensionJuan Carlos Muñoz Grajales0Departamento de Matemáticas, Universidad del Valle, Calle 13 Nro 100-00, Cali, ColombiaWe establish existence and uniqueness of solutions to the Cauchy problem associated with a new one-dimensional weakly-nonlinear, weakly-dispersive system which arises as an asymptotical approximation of the full potential theory equations for modelling propagation of small amplitude water waves on the surface of a shallow channel with variable depth, taking into account the effect of surface tension. Furthermore, numerical schemes of spectral type are introduced for approximating the evolution in time of solutions of this system and its travelling wave solutions, in both the periodic and nonperiodic case.http://dx.doi.org/10.1155/2015/805625 |
| spellingShingle | Juan Carlos Muñoz Grajales Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension International Journal of Differential Equations |
| title | Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension |
| title_full | Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension |
| title_fullStr | Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension |
| title_full_unstemmed | Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension |
| title_short | Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension |
| title_sort | propagation of water waves over uneven bottom under the effect of surface tension |
| url | http://dx.doi.org/10.1155/2015/805625 |
| work_keys_str_mv | AT juancarlosmunozgrajales propagationofwaterwavesoverunevenbottomundertheeffectofsurfacetension |