Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation
It is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic both in space and time coordinates; such solutions generalize...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2021-02-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2021.599146/full |
| _version_ | 1819284273923883008 |
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| author | Dmitry E. Pelinovsky |
| author_facet | Dmitry E. Pelinovsky |
| author_sort | Dmitry E. Pelinovsky |
| collection | DOAJ |
| description | It is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic both in space and time coordinates; such solutions generalize the standing waves which have the time-independent and space-periodic wave function modulus. Similar to other waves in the NLS equation, the double-periodic solutions are spectrally unstable and this instability is related to the bands of the Lax spectrum outside the imaginary axis. A simple numerical method is used to compute the unstable spectrum and to compare the instability rates of the double-periodic solutions with those of the standing periodic waves. |
| first_indexed | 2024-12-24T01:44:46Z |
| format | Article |
| id | doaj.art-ccba69008ae94912a17f7ed7bf39f53b |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-24T01:44:46Z |
| publishDate | 2021-02-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-ccba69008ae94912a17f7ed7bf39f53b2022-12-21T17:21:54ZengFrontiers Media S.A.Frontiers in Physics2296-424X2021-02-01910.3389/fphy.2021.599146599146Instability of Double-Periodic Waves in the Nonlinear Schrödinger EquationDmitry E. PelinovskyIt is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic both in space and time coordinates; such solutions generalize the standing waves which have the time-independent and space-periodic wave function modulus. Similar to other waves in the NLS equation, the double-periodic solutions are spectrally unstable and this instability is related to the bands of the Lax spectrum outside the imaginary axis. A simple numerical method is used to compute the unstable spectrum and to compare the instability rates of the double-periodic solutions with those of the standing periodic waves.https://www.frontiersin.org/articles/10.3389/fphy.2021.599146/fullmodulational instabilitydouble-periodic solutionsFloquet spectrumnonlinear Schrödinger equationstanding waves |
| spellingShingle | Dmitry E. Pelinovsky Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation Frontiers in Physics modulational instability double-periodic solutions Floquet spectrum nonlinear Schrödinger equation standing waves |
| title | Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation |
| title_full | Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation |
| title_fullStr | Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation |
| title_full_unstemmed | Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation |
| title_short | Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation |
| title_sort | instability of double periodic waves in the nonlinear schrodinger equation |
| topic | modulational instability double-periodic solutions Floquet spectrum nonlinear Schrödinger equation standing waves |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2021.599146/full |
| work_keys_str_mv | AT dmitryepelinovsky instabilityofdoubleperiodicwavesinthenonlinearschrodingerequation |