Modulational stability of Korteweg-de Vries and Boussinesq wavetrains
The modulational stability of both the Korteweg-de Vries (KdV) and the Boussinesq wavetrains is investigated using Whitham's variational method. It is shown that both KdV and Boussinesq wavetrains are modulationally stable. This result seems to confirm why it is possible to transform the KdV eq...
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000691 |
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| _version_ | 1832545657282363392 |
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| author | Bhimsen K. Shivamoggi Lokenath Debnath |
| author_facet | Bhimsen K. Shivamoggi Lokenath Debnath |
| author_sort | Bhimsen K. Shivamoggi |
| collection | DOAJ |
| description | The modulational stability of both the Korteweg-de Vries (KdV) and the
Boussinesq wavetrains is investigated using Whitham's variational method. It is shown that both KdV and Boussinesq wavetrains are modulationally stable. This result seems to confirm why it is possible to transform the KdV equation into a nonlinear Schrödinger equation with a repulsive potential. A brief discussion of Whitham's variational method is included to make the paper self-contained to some extent. |
| format | Article |
| id | doaj-art-9010f33c3c9f4f6cbb9bff5da81df6a1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9010f33c3c9f4f6cbb9bff5da81df6a12025-02-03T07:25:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016481181710.1155/S0161171283000691Modulational stability of Korteweg-de Vries and Boussinesq wavetrainsBhimsen K. Shivamoggi0Lokenath Debnath1Physical Research Laboratory, Ahmedabad 380 009, IndiaDepartment of Mathematics, University of Central Florida, Orlando 32816, Florida, USAThe modulational stability of both the Korteweg-de Vries (KdV) and the Boussinesq wavetrains is investigated using Whitham's variational method. It is shown that both KdV and Boussinesq wavetrains are modulationally stable. This result seems to confirm why it is possible to transform the KdV equation into a nonlinear Schrödinger equation with a repulsive potential. A brief discussion of Whitham's variational method is included to make the paper self-contained to some extent.http://dx.doi.org/10.1155/S0161171283000691nonlinear wavesWhitham's variational principleKdV and Boussinesq wavetrainsmodulational stabilitynonlinear Schrödinger equation. |
| spellingShingle | Bhimsen K. Shivamoggi Lokenath Debnath Modulational stability of Korteweg-de Vries and Boussinesq wavetrains International Journal of Mathematics and Mathematical Sciences nonlinear waves Whitham's variational principle KdV and Boussinesq wavetrains modulational stability nonlinear Schrödinger equation. |
| title | Modulational stability of Korteweg-de Vries and Boussinesq wavetrains |
| title_full | Modulational stability of Korteweg-de Vries and Boussinesq wavetrains |
| title_fullStr | Modulational stability of Korteweg-de Vries and Boussinesq wavetrains |
| title_full_unstemmed | Modulational stability of Korteweg-de Vries and Boussinesq wavetrains |
| title_short | Modulational stability of Korteweg-de Vries and Boussinesq wavetrains |
| title_sort | modulational stability of korteweg de vries and boussinesq wavetrains |
| topic | nonlinear waves Whitham's variational principle KdV and Boussinesq wavetrains modulational stability nonlinear Schrödinger equation. |
| url | http://dx.doi.org/10.1155/S0161171283000691 |
| work_keys_str_mv | AT bhimsenkshivamoggi modulationalstabilityofkortewegdevriesandboussinesqwavetrains AT lokenathdebnath modulationalstabilityofkortewegdevriesandboussinesqwavetrains |