Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation
In many physical contexts, notably including deep-water waves, modulation instability in one space dimension is often studied by using the nonlinear Schrödinger equation. The principal solutions of interest are solitons and breathers which are adopted as models of wave packets. The Peregrine breathe...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/7/7/233 |
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| author | Montri Maleewong Roger H. J. Grimshaw |
| author_facet | Montri Maleewong Roger H. J. Grimshaw |
| author_sort | Montri Maleewong |
| collection | DOAJ |
| description | In many physical contexts, notably including deep-water waves, modulation instability in one space dimension is often studied by using the nonlinear Schrödinger equation. The principal solutions of interest are solitons and breathers which are adopted as models of wave packets. The Peregrine breather in particular is often invoked as a model of a rogue wave. In this paper, we add a linear growth term to the nonlinear Schrödinger equation to model the amplification of propagating wave groups. This is motivated by an application to wind-generated water waves, but this forced nonlinear Schrödinger equation potentially has much wider applicability. We describe a series of numerical simulations which in the absence of the forcing term would generate solitons and/or breathers. We find that overall the effect of the forcing term is to favour the generation of solitons with amplitudes growing at twice the linear growth rate over the generation of breathers. |
| first_indexed | 2024-03-09T03:26:47Z |
| format | Article |
| id | doaj.art-cc3b1d4d9cd74bba8ff246953ee98247 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-09T03:26:47Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-cc3b1d4d9cd74bba8ff246953ee982472023-12-03T15:02:11ZengMDPI AGFluids2311-55212022-07-017723310.3390/fluids7070233Amplification of Wave Groups in the Forced Nonlinear Schrödinger EquationMontri Maleewong0Roger H. J. Grimshaw1Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, ThailandDepartment of Mathematics, University College London, London WC1E 6BT, UKIn many physical contexts, notably including deep-water waves, modulation instability in one space dimension is often studied by using the nonlinear Schrödinger equation. The principal solutions of interest are solitons and breathers which are adopted as models of wave packets. The Peregrine breather in particular is often invoked as a model of a rogue wave. In this paper, we add a linear growth term to the nonlinear Schrödinger equation to model the amplification of propagating wave groups. This is motivated by an application to wind-generated water waves, but this forced nonlinear Schrödinger equation potentially has much wider applicability. We describe a series of numerical simulations which in the absence of the forcing term would generate solitons and/or breathers. We find that overall the effect of the forcing term is to favour the generation of solitons with amplitudes growing at twice the linear growth rate over the generation of breathers.https://www.mdpi.com/2311-5521/7/7/233wind wavesbreatherssolitonnonlinear Schrodingerroguemodulation instablity |
| spellingShingle | Montri Maleewong Roger H. J. Grimshaw Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation Fluids wind waves breathers soliton nonlinear Schrodinger rogue modulation instablity |
| title | Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation |
| title_full | Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation |
| title_fullStr | Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation |
| title_full_unstemmed | Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation |
| title_short | Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation |
| title_sort | amplification of wave groups in the forced nonlinear schrodinger equation |
| topic | wind waves breathers soliton nonlinear Schrodinger rogue modulation instablity |
| url | https://www.mdpi.com/2311-5521/7/7/233 |
| work_keys_str_mv | AT montrimaleewong amplificationofwavegroupsintheforcednonlinearschrodingerequation AT rogerhjgrimshaw amplificationofwavegroupsintheforcednonlinearschrodingerequation |